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In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0, 1]. By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the uniqueness and existence of the classical solution to higher-order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher order boundary value problems. Our study is based on Green’s functions corresponding to the five different types of two-point boundary value problems. In addition, some applications of the obtained inequalities are given. [ABSTRACT FROM AUTHOR]

This paper addresses the second-order nonlocal dynamic thermistor problem with two-point boundary conditions on time scales. Utilizing the fixed point theorems by Schaefer and Rus, we establish some sufficient conditions for the existence and uniqueness of solutions. Furthermore, we discuss the continuous dependence of solutions and four types of Ulam stability. We provide examples to support the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, the Neumann boundary value problem for the Beltrami operator is explicitly solved in a circular ring domain, solvability conditions for this problem are also given in explicit forms. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part as combinations of the Cauchy-Riemann and the Beltrami operators is investigated. [ABSTRACT FROM AUTHOR]

In this work, we are interested in a boundary value problem (BVP) generated by a Klein-Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example. [ABSTRACT FROM AUTHOR]

In this paper, we consider a regular fractal Sturm–Liouville boundary value problem. We prove the selfadjointness of the differential operator which is generated by the F α -derivative introduced in [32]. We obtained the F α - analogue of Liouville’s theorem, and we show some properties of eigenvalues and eigenfunctions. We present examples to demonstrate the efficiency and applicability of the obtained results. The findings of this paper can be regarded as a contribution to an emerging field. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to state and prove a general nonnegativity principle in the framework of multiterm fractional differential equations, which we use to investigate some iterative monotone sequences of lower and upper solutions to a certain fractional eigenvalue problem. The obtained results can be easily extended to fractional differential equations of distributed orders since the latter are the natural extension of multiterm fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper we consider a boundary value problem for a loaded fractional diffusion equation. The loaded term has the form of the Riemann-Liouville fractional derivative or integral. The BVP is considered in the open right upper quadrant. The problem is reduced to an integral equation that, in some cases, belongs to the pseudo-Volterra type, and its solvability depends on the order of differentiation in the loaded term and the behavior of the support line of the load in a neighborhood of the origin. All these cases are considered. In particular, we establish sufficient conditions for the unique solvability of the problem. Moreover, we give an example showing that violation of these conditions can lead to nonuniqueness of the solution. [ABSTRACT FROM AUTHOR]

The main goal of this work is to study an initial boundary value problem for a Kirchhoff-type equation with nonlinear boundary delay and source terms. This paper is devoted to prove the global existence, decay, and the blow up of solutions. To the best of our knowledge, there are not results on the Kirchhoff type-equation with nonlinear boundary delay and source terms. [ABSTRACT FROM AUTHOR]

This paper deals with nonself-adjoint second-order differential operators with two constant delays from [ π 2 , π ) and two real-valued potentials from L2[0, π] . An inverse spectral problem of recovering operators from the spectra of four boundary value problems is studied. [ABSTRACT FROM AUTHOR]

This paper establishes Lyapunov-type inequalities for a family of two-point (n, p) -type boundary value problems for Riemann--Liouville fractional differential equations. To demonstrate how the findings can be applied, we provide a few examples, one of which is a fractional differential equation with delay. [ABSTRACT FROM AUTHOR]

This paper deals with the geometrical singularities of the weak solution of the mixed boundary value problem governed by the stationary Stokes system in two-dimensional nonsmooth domains with corner points and points at which the type of boundary conditions changes. The presence of these points on the boundary generally generates local singularities in the solution. We will see the impact of the geometrical singularities of the boundary or the mixed boundary conditions on the qualitative properties of the solution including its regularity. Moreover, the asymptotic singular representations for the solution which inherently depend on the zeros of certain transcendental functions are presented. [ABSTRACT FROM AUTHOR]

In this paper, a matrix-collocation method which uses the Euler polynomials is introduced to find the approximate solutions of singularly perturbed two-point boundary-value problems (BVPs). A system of algebraic equations is obtained by converting the boundary value problem with the aid of the collocation points. After this algebraic system, the coefficients of the approximate solution are determined. This error analysis includes two theorems which consist of an upper bound of errors and an error estimation technique. The present method and error analysis are applied to three numerical examples of singularly perturbed two-point BVPs. Numerical examples and comparisons with other methods are given. These applications and comparisons show that the method gives effective results. [ABSTRACT FROM AUTHOR]

In this paper, we study boundary value problems for the impulsive integro-differential equations via 1-fractional derivative. The contraction mapping concept and Schaefer's fixed point theorem are used to produce the main results. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam-Hyers-Rassias stability of the solution to the proposed system. [ABSTRACT FROM AUTHOR]

In this paper, the Dirac type integro differential system with a nonlocal integral boundary condition is considered. First, we derive the asymptotic expressions for the solutions and large eigenvalues. Second, we provide asymptotic expressions for the nodal points and prove that a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered differential system. We also provide an effective procedure for solving the inverse nodal problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and uniqueness for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations. By the fixed point theorem in Banach algebra, an existence theorem for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is given. Further, a uniqueness result for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is proved due to Banach's contraction principle. Further, we give three examples to verify the main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of four-point boundary value problems of fractional q-difference equation with p-Laplacian operator which is the first time to be studied and is extended from a bending elastic beam equation. By Avery-Peterson theorem and the method of lower and upper solutions associated with monotone iterative technique, we obtain some sufficient conditions for the existence of multiple positive solutions. As applications, examples are presented to illustrate the main results. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to obtain some new existence results of solutions for a boundary value problem for a (p,q) -difference equations with integral conditions, by using fixed point theorems. Examples illustrating the main results are also presented. [ABSTRACT FROM AUTHOR]

This paper deals with infinite system of nonlinear two-point tempered fractional order boundary value problems ... where j ∈ {1, 2, 3, ...}, ℓ ≥ 0, 0RL픻z*,ℓ denotes the Riemann-Liouville tempered fractional derivative of order * ∈ {δ1, δ2}, V(z) = (Vj(z))j=1∞, φj : [0, T] → [0, T] are continuous and we derive sufficient conditions for the existence of solutions to the system via the Hausdorff measure of noncompactness and Meir-Keeler fixed point theorem in tempered sequence spaces. [ABSTRACT FROM AUTHOR]

In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales TαΔ[ TβΔ (Vn(t))] = φ(t) fn(Vn+1(t)), t ∈ (0, 1)핋, 1 < α, β ≤ 2 V1(t) = Vl+1 (t), t ∈ (0, 1)핋, n = 1, 2, ..., l, satisfying two-point Riemann--Stieltjes integral boundary conditions Vn(0) = 0, Vn(1) = ∫0¹ Vn(τ)g(τ), n = 1, 2, ..., l, (TβΔVn)(0) = 0, (TβΔVn) (1) = ∫0¹ (TβΔVn) (τ)g(τ), n = 1, 2, ..., l, where T*Δ denotes the conformable fractional derivative of order * ∈ {α, β} on time scale T, by an application of Krasnoselskii's fixed point theorem on a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional p-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; 24: 295-304]. [ABSTRACT FROM AUTHOR]

In this paper, we establish new Lyapunov-type inequalities for (n + 1)st order nonlinear differential equation including p-relativistic operator and q -prescribed curvature operator under the antiperiodic boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence--uniqueness of solution to the second-order linear Fredholm integrodifferential equation (FIDE) with Dirichlet boundary condition by hybridizable discontinuous Galerkin (HDG) method. A key property of these methods is to eliminate all internal degrees of freedom and to construct a linear system that only includes globally coupled unknowns at the element interfaces. After designing and implementing HDG algorithm, we provide some necessary and sufficient conditions based on the stabilization parameter and kernel function to guarantee the existence-uniqueness of the approximate solution. Then, some numerical examples are carried out to assess the performance of the present method. When comparing with existing some methods in literature, the experimental studies verify the reliability and feasibility of the HDG method for the problem under consideration. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse boundary value problem for a partial differential equation of third order with nonlocal boundary conditions, including an integral condition. Using analytical and operator-theoretic methods, as well as the Fourier method, the existence and uniqueness of the classical solution of this problem is proved. [ABSTRACT FROM AUTHOR]

By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the Leray-Schauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411). [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the following discrete problem first { −Δ2u(t − 1) = λp(t)f(u(t)), t ∈ [1,N − 1]Z, Δu(0) = u(N) = 0, where N > 2 is an integer, λ > 0 is a parameter, p : [1,N−1]Z → R is a sign-changing function, f : [0,+∞) → [0,+∞) is a continuous and nondecreasing function. Δu(t) = u(t+1)−u(t), Δ2u(t) = Δ(Δu(t)) . By using the iterative method and Schauder’s fixed point theorem, we will show the existence of nonnegative solutions to the above problem. Furthermore, we obtain the existence of nonnegative solutions for discrete Robin systems with indefinite weights. [ABSTRACT FROM AUTHOR]

In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator. [ABSTRACT FROM AUTHOR]

In this paper, we consider a mixed boundary value problem to a class of quasi-linear elliptic operators containing a p-Laplace operator. We show the existence of a unique weak solution and an estimate. We also demonstrate the continuity of the solution on the given data. Moreover, we consider the dual problem. [ABSTRACT FROM AUTHOR]

In this paper we give definition of m-fold completeness and prove a theorem on completeness of elementary generalized solution of corresponding boundary value problems at which the equation describes the process of corrosive fracture of metals in aggressive media and the principal part of the equation has multiple characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given. [ABSTRACT FROM AUTHOR]

In this paper, we consider some third-order operators with transmission conditions. In particular, it is shown that such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operators associated with the differential operators. After showing that the eigenvalues of the problems are real and discrete we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data. [ABSTRACT FROM AUTHOR]

The present paper considers the equilibrium theory of thermo-microstretch elastic solids with microtemperatures. The method to solve the Neumann-type boundary value problem (BVP) for the whole space with spherical cavity is presented. The solution of this BVP in the form of absolutely and uniformly convergent series is obtained. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to examine the scattering analysis of a multiplicative Sturm-Liouville boundary value problem. Firstly, we find the Jost solution of this problem and give the Jost function to construct the scattering function of the problem. Secondly, we obtain asymptotic equations for Jost solution and investigate some properties of the Jost function. Moreover, we present other solutions of the problem by giving the relations between these solutions and Jost solution. Finally, we define the scattering function of this problem by using the Jost function and examine the basic properties of the scattering function. [ABSTRACT FROM AUTHOR]

This paper deals with the multiplicity results of positive solutions of one-dimensional singular p-Laplace equation (φp(u′(t)))′ + a(t)f(t, u(t), u′(t)) = 0, 0 < t < 1 subject to the nonlinear boundary conditions αφp(u(0)) - βφp(u′(ξ)) = 0, γφp (u(1)) + δφp(u′(η)) = 0, where φp(x) = |x|p-2x, p > 1. By using the Avery-Peterson fixed point theorem, sufficient conditions for the existence of at least three positive solutions to the boundary value problem mentioned above are obtained. [ABSTRACT FROM AUTHOR]

This paper deals with the positive solutions of nonlinear boundary value problems in Banach spaces. By using fixed point index theory, some sufficient conditions for the existence of at least one or two positive solutions to boundary value problems in Banach spaces are obtained. An example illustrating the main results is given. [ABSTRACT FROM AUTHOR]

The concept of the ‘relation of comparability’ was introduced by Maillet in [7], who showed that if α,β are comparable Liouville numbers then each of the numbers α+β, α-β, αβ and α/β is either a rational or Lioville number. Moreover those which are Liouville numbers are comparable aamong theem and toα and β Maillet's proof uses in an essential way the transitivity of the comparability relation. Unfortunately, as the comparability relation is not transitive, his proof is defective. In this paper, without using the comparability relation, we obtain some uncountable subfields of p-adic numbers field, Qp. In [1] using a different notion of comparability, Alnıaçık was able to define some uncountable subfields of C. In this paper, without using comparability relation, we define irregular semistrong p-adic Um numbers and obtain some uncountable subfields of p-adic numbers field Qp. [ABSTRACT FROM AUTHOR]

In this work, we apply Leray-Schauder continuation principle to establish the existence of at least one solution to the third order p-Laplacian boundary value problem on an unbounded domain of the form (w(t)φp(u ′′ (t))) ′ = K(t, u(t), u ′ (t), u ′′ (t)), t ∈ (0,∞) u(0) = 0, u ′ (0) = Σm i=1 αi ∫ ξi 0 u(t)dt, lim t→∞ (w(t)φp(u ′′ (t)) = 0 under the nonresonant condition Σm i=1 αiξ² ̸= 2. [ABSTRACT FROM AUTHOR]

Using the coincidence degree theory of Mawhin and constructing appropriate operators, we investigate the existence of solutions to Hadamard fractional differential equations (FRDEs) at resonance ... where 1 < γ < 2, f: [1, e]×R² → R satisfies Carathéodory conditions, ∫e1 u(t)dA(t) is the Riemann-Stieltjes integration, and (HDγu) is the Hadamard fractional derivation of u of order γ. An example is included to illustrate our result. [ABSTRACT FROM AUTHOR]

One nonlocal boundary value problem for the Laplace equation in a bounded domain is considered in this work. The concept of a strong solution to this problem is introduced. The correct solvability of this problem in the Sobolev spaces generated by the weighted mixed norm is proved by the Fourier method. In a classic statement, this problem has been earlier considered by E.I.Moiseev [34]. A similar problem has been treated by M.E.Lerner and O.A.Repin [30]. [ABSTRACT FROM AUTHOR]

We study the dynamics of a Neumann boundary value problem arising in fluid dynamics. We prove the nonexistence, existence and uniqueness of positive solutions under suitable conditions. At the same time, under stricter conditions, we also obtain the dynamic properties of the Neumann boundary value problem, such as the stability and instability of positive solutions. The methods of proof mainly involve the upper and lower solutions method, eigenvalue theory and some analysis techniques. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the half inverse problem for the Sturm-Liouville operator with boundary conditions dependent on the spectral parameter and show that if q(x) is prescribed on [π/2, π], then one spectrum is sufficient to determine the potential q(x) on the whole interval [0,π] and coefficient function a1λ+b1/c1λ+d1 of the boundary condition. [ABSTRACT FROM AUTHOR]

The present paper is devoted to a proof of the existence and uniqueness of strong solution for a high order boundary value problem with integral condition. The proof is based by a priori estimate and on the density of the range of the operator generated by the studied problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlocal parabolic equation ut = Δu + λH(1 - u)/(∫Ap,R H(1 - u)dx)², x ∈ Ap,R ⊂ ℝ², t > 0, with a homogeneous Dirichlet boundary condition, where λ is a positive parameter, H is the Heaviside function and Ap,R is an annulus. It is shown for the radial symmetric case that: there exist two critical values λ* and λ*, so that for 0 < λ < λ*, u(x, t) is global in time and the unique stationary solution is globally asymptotically stable; for λ* < λ < λ* there also exists a steady state and u(x, t) is global in time; while for λ > λ* there is no steady state and u(x, t) "blows up" (in some sense) for any appropriate (u0 (x) ≤ 1) initial data. [ABSTRACT FROM AUTHOR]

This paper is concerned with the one-dimensional p-Laplacian multi-point boundary value problem on time scales 핋: (ψp(uΔ))∇ + h(t)f(u) = 0 ∈ [0, T] 핋, subject to multi-point boundary conditions Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. or Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. where ψp(u) is p-Laplacian operator, i.e., Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. and satisfy Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. Some new sufficient conditions are obtained for the existence of at least one positive solution by using Krasnosel'skii's fixed-point theorem and new sufficient conditions are obtained for the existence of twin, triple or arbitrary odd positive solutions by using generalized Avery and Henderson fixed-point theorem and Avery-Peterson fixed-point theorem. Our results include and extend some known results. As applications, two examples are given to illustrate the main results and their differences. These results are new even for the special cases of continuous and discrete equations, as well as in the general time scale setting. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for nonlinear Lidstone boundary value problems by using the monotone method on time scale and also we show the existence of at least one positive solution if f is either superlinear or sublinear by the fixed point theorem in a Banach space. [ABSTRACT FROM AUTHOR]

In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green's functions are investigated and existence results for positive solutions of the nonlinear boundary value problem are established. Upper and lower bounds for these positive solutions also are given. [ABSTRACT FROM AUTHOR]

This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example. [ABSTRACT FROM AUTHOR]

In this paper, we consider a condition on subspaces in order to improve bounds given in Bernstein's lethargy theorem for Banach spaces. Let d1 ≥ d2 ≥ ⋯ dn ≥ ⋯ > 0 be an infinite sequence of numbers converging to 0, and let Y1 ⊂ Y2 ⊂ ⋯ ⊂ Yn ⊂ ⋯ ⊂ X be a sequence of closed nested subspaces in a Banach space X with the property that ...n ⊂ Yn+1 for all n ≥ 1. We prove that for any c ∈ (0, 1] there exists an element xc ∈ X such that ... Here, ... where the sequence {an} is defined as: for all n ≥ 1, ... in which each point qn is taken from Yn+1 \ Yn, and satisfies ... an > 0. The sequence {ni}i≥1 is given by .... [ABSTRACT FROM AUTHOR]

In this paper, a nonpolynomial spline technique is applied to solve the ninth order linear special case boundary value problems. The end conditions are derived to complete the definition of a spline. Three examples are numerically illustrated to check the efficiency of the method. The comparative analysis shows that the proposed technique gives better results than the homotopy perturbation method and the modified variational iteration method. [ABSTRACT FROM AUTHOR]