Search

In this article, we prove the existence and localization of solutions for a vector impulsive Dirichlet problem with multivalued upper-Carathéodory right-hand side. The result is obtained by combining the continuation principle with a bound sets technique. The main theorem is illustrated by an application to the forced pendulum equation with viscous damping term and dry friction coefficient. [ABSTRACT FROM AUTHOR]

In this article we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. Then the maximum number of limit cycles that bifurcate from these periodic orbits is 6 and it is reached. This family of centers completes the study of the limit cycles which can bifurcate from periodic orbits of all centers of the weight-homogeneous polynomial differential systems of weight-degree 3 when perturbed in the class of all polynomial differential systems having the same degree and whose average function of first order is not zero. [ABSTRACT FROM AUTHOR]

We find an explicit formula for the coefficients of the generalized Maclaurin series for sinp provided p > 2 is an integer. Our method is based on an expression of the n-th derivative of sinp in the form ... where cosp stands for the first derivative of sinp. The formula allows us to compute the nonzero coefficients ... [ABSTRACT FROM AUTHOR]

We study the existence, uniqueness, and asymptotic behavior of positive continuous solutions to the fractional Navier boundary-value problem Dβ (Dαu)(x) = –p(x)uσ, ∊(0,1), lim x→0 x1-β Dα u(x) = 0, u(1) = 0, where α, β ∊ (0,1] such that α + β > 1, Dβ and Dα stand for the standard Riemann-Liouville fractional derivatives, σ ∊ (–1,1) and p being a nonnegative continuous function in (0,1) that may be singular at x = 0 and satisfies some conditions related to the Karamata regular variation theory. Our approach is based on the Schäuder xed point theorem. [ABSTRACT FROM AUTHOR]

We present new criteria for asymptotic stability of two classes of nonlinear neutral delay differential equations. By using two auxiliary functions on a contraction condition, we extend the results in [12]. Also we give two examples that illustrate our results. [ABSTRACT FROM AUTHOR]

This article concerns a general fractional differential equation of order between 1 and 2. We consider the cases where the nonlinear term contains or does not contain other (lower order) fractional derivatives (of Riemann-Liouville type). Moreover, the nonlinearity involves also a nonlinear non-local in time term. The case where this non-local term has a singular kernel is treated as well. It is proved, in all these situations, that solutions approach power type functions at infinity. [ABSTRACT FROM AUTHOR]

In this article, we study the inverse problem for Sturm-Liouville operators with boundary conditions dependent on the spectral parameter. We show that the potential q(x) and coefficient a1 λ + b1/ c1 λ + d1 functions can be uniquely determined from the particular set of eigenvalues. [ABSTRACT FROM AUTHOR]

"Sharp localized" solutions (i.e. with compact support for each given time t) of a singular nonlinear type Schrödinger equation in the whole space ℝN are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that f (t, x) = t-(p-2)/2F(t-1/2x) for some complex exponent p and for some profile function F which is assumed to be with compact support in ℝN. We show the existence of solutions of the form u(t, x) = tp/2U(t-1/2x), with a profile U, which also has compact support in ℝN. The proof of the localization of the support of the profile U uses some suitable energy method applied to the stationary problem satisfied by U after some unknown transformation. [ABSTRACT FROM AUTHOR]

In this article, we study a class of nonlinear elliptic systems in regular domains of Rn(n ≥ 3) with compact boundary. More precisely, we prove the existence of bounded positive continuous solutions to the system Δu = λf(., u, v), Δv = μg(., u, v), subject to some Dirichlet conditions. Our approach is essentially based on properties of functions in a Kato class K∞(D) and the Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

This article concerns the decay of solutions of the semi-linear wave equation utt + δut - Φ(x)Δu = λu|u|β-1 x ∈ ℝN t ≥ 0 Introducing an appropriate Lyaponuv function, we find exponential decay for certain initial data. [ABSTRACT FROM AUTHOR]

In this article we consider an n-dimentional thermoelastic system with a viscoelastic damping localized on a part of the boundary. We establish an explicit and general decay rate result that allows a larger class of relaxation functions and generalizes previous results existing in the literature. [ABSTRACT FROM AUTHOR]

We study the existence of multiple solutions to the boundary value problem d/dt(1/20Dt-β(u'(t)) + 1/2tDT-β (u'(t)))+ λ∇F(t, u(t)) = 0, t ∈ [0, T], u(0) = u(T) = 0, where T > 0, λ > 0 is a parameter, 0 ≤ β < 1, 0Dt-β and tDT-β are, respectively, the left and right Riemann-Liouville fractional integrals of order β, F : [0, T] x ℝN → R is a given function. Our interest in the above system arises from studying the steady fractional advection dispersion equation. By applying variational methods, we obtain sufficient conditions under which the above equation has at least three solutions. Our results are new even for the special case when β = 0. Examples are provided to illustrate the applicability of our results. [ABSTRACT FROM AUTHOR]

In this article we consider a Cauchy problem of a nonlinear viscoelastic equation of order four. Under suitable conditions on the initial data and the relaxation function, we prove polynomial and logarithmic decay of solutions. [ABSTRACT FROM AUTHOR]

In this article we introduce and study a new class of functions called Stepanov-like pseudo-almost automorphic functions with variable exponents, which generalizes in a natural way classical Stepanov-like pseudo-almost automorphic spaces. Basic properties of these new spaces are investigated. The existence of pseudo-almost automorphic solutions to some first-order diffeerential equations with Sp,q(x)-pseudo-almost automorphic coefficients will also be studied. [ABSTRACT FROM AUTHOR]

We are concerned with the oscillatory behavior of the solutions of a generalized Euler differential equation where the nonlinearities satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub(super) linearity are assumed. Some implicit necessary and sufficient conditions and some explicit sufficient conditions are given for all nontrivial solutions of this equation to be oscillatory or nonoscillatory. Also, it is proved that solutions of the equation are all oscillatory or all nonoscillatory and cannot be both. [ABSTRACT FROM AUTHOR]

In this article, we are interested in the existence of positive solutions for the Kirchhoff type problems -M(∫Ω|∇u|p dx)∇pu = λf(u) in Ω u > 0 in Ω, u = 0 on ∂Ω, where 1 < p < N, M : R+ → R+ is a continuous and increasing function, λ is a parameter, f : [0, +∞) → R is a C¹ nondecreasing function satisfying f(0) < 0 (semipositone). Our proof is based on the sub- and super-solutions techniques. [ABSTRACT FROM AUTHOR]

Using variational arguments, we study the existence and multiplicity of solutions for the degenerate nonlocal differential equation -M(∫Ω |x|-ap|∇u|pdx) div (|x|-ap|∇u|p-2∇u)= |x|-p(a+1)+cf(x; u) in Ω u = 0 on ∂Ω, where Ω ⊂ RN (N ≥ 3) and the function M may be zero at zero. [ABSTRACT FROM AUTHOR]

By using a modified function technique and variational methods, we establish the existence of infinitely many homoclinic solutions for a second-order Hamiltonian system ü - L(t)u + Fu(t, u) = 0, for all t ∈ ℝ, where no coercive condition for F(t, u) at infinity is imposed. [ABSTRACT FROM AUTHOR]

In this work, we study the existence of positive solutions to the singular problem -Δpu = λm(x)f(u) - u-α in Ω, u = 0 on ∂Ω, where λ is positive parameter, Ω is a bounded domain with smooth boundary, 0 < α < 1, and f : [0,∞] → R is a continuous function which is asymptotically p-linear at ∞. The weight function is continuous satisfies m(x) > m0 > 0, ||m|| ∞ < ∞. We prove the existence of a positive solution for a certain range of λ using the method of sub-supersolutions. INSET: x. [ABSTRACT FROM AUTHOR]

In this article we consider a degenerate Kirchhoff equation wave equation with a weak frictional damping, (|ut|1-2ut)t - (∫;Ω|∇xu|² dx)γ∇xu + α(t)g(ut) = 0. We prove general stability estimates using some properties of convex functions, without imposing any growth condition at the frictional damping term. [ABSTRACT FROM AUTHOR]

This article concerns the long time behavior of solutions to nonlocal delay equations when the initial values decay slowly at infinity towards the unstable steady state. By constructing proper auxiliary functions, it is proved that the lower bounds of asymptotic speed for spreading is larger any given positive constant, which implies the fast propagation. [ABSTRACT FROM AUTHOR]

We establish some oscillation criteria for the solutions to forced higher-order differential equations. We do not assume that the forcing term is the n-th derivative of an oscillatory function, and do not assume that the coefficients are of a definite sign. Our results are illustrated with examples. [ABSTRACT FROM AUTHOR]

We apply the averaging theory of first and second order to a generalized Liénard differential equation. Our main result shows that for any n, m ≥ 1 there are differential equations Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., with f and g polynomials of degree n and m respectively, having at most [n/2] and n+1 max{[(n - 1)/2] + [m/2], [n + (-1)n+1/2]} limit cycles, where [·] denotes the integer part function. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of solutions to the differential equation fn(z) + P(f) = P₁eh1 + P₂eh2 , where n ≥ 2 is an positive integer, f is a transcendental entire function, P(f) is a differential polynomial in f of degree less than or equal n - 1, P₁, P₂ are small functions of ez, h₁, h₂ are polynomials, and z is in the open complex plane C. Our results extend those obtained by Li [6, 7, 8, 9]. [ABSTRACT FROM AUTHOR]

In this article, we study the growth of solutions to the differential equation Fk + (Ak-1(z)eΡk-1(z)eλzm + Bk-1(z)) fk-1 + ... + (A0(z)eΡ0(z)eλzm + B0(z))f = 0, where λ ∈ C*, m ≥ 2 is an integer and maxj=0,...,k-1{deg Ρj (z)} < m, Aj, Bj (j = 0, . . . , k - 1) are entire functions of orders less than m. [ABSTRACT FROM AUTHOR]

We study the solutions to the delay differential equation equation ẋ(t) = -a(t)x(t - h), where the coefficient a(t) is not necessarily positive. It is proved that this equation is exponentially stable provided that a(t) = b+c(t) for some positive constant b less than π/(2h), and the integral ∫0t c(s)ds is sufficiently small for all t > 0. In this case the 3/2-stability theorem is improved. [ABSTRACT FROM AUTHOR]

We find necessary and sufficient conditions for the differential equation u(n)(t) = Au(t) + f(t), t ∈ ℝ to have a unique almost periodic solution. Some applications are also given. [ABSTRACT FROM AUTHOR]

This article presents new oscillation criteria for the second-order delay differential equation (p(t)(x'(t))α)' + q(t)xα(t - τ) + n∑i=1 qi(t)xαi (t - τ) = e(t) where τ ≥ 0, p(t) ∈ C¹[0,∞), q(t), qi(t), e(t) ∈ C[0,∞), p(t) > 0, α1 > ⋯ > αm > α > αm+1 > ⋯ > αn > 0 (n > m ≥ 1), α1, ..., αn and α are ratio of odd positive integers. Without assuming that q(t), qi(t) and e(t) are nonnegative, the results in have been extended and a mistake in the proof of the results in is corrected. [ABSTRACT FROM AUTHOR]

We extend Painlevé's determinateness theorem to first-order ordinary differential equations in the complex domain, with known terms allowed be multivalued in the dependent variable. The multivaluedness is supposed to be resolved by proper coverings. [ABSTRACT FROM AUTHOR]

Using the theory of the fixed point index in a cone and the Leray-Schauder degree, this paper investigates the existence and multiplicity of nontrivial solutions for a class of fourth order m-point boundary-value problems. [ABSTRACT FROM AUTHOR]

In this work we give necessary and sufficient conditions for having a maximum principle for cooperative elliptic systems involving p-Laplacian operator on the whole ℝN. This principle is then used to yield solvability for the cooperative elliptic systems by an approximation method. [ABSTRACT FROM AUTHOR]

In this article, we consider a uniqueness theorem of Holmgren type for p-th order Kovalevskaja linear partial differential equations whose coefficients are Gevrey functions. We prove that the only Cp-solution to the zero initial-valued problem is the identically zero function. To prove this result we use the uniqueness theorem for higher-order ordinary differential equations in Banach scales. [ABSTRACT FROM AUTHOR]

In this article we consider the existence, uniqueness and positivity of a first order non-linear periodic differential equation. The main tool employed is the Krasnosel'skiĭ's fixed point theorem for the sum of a completely continuous operator and a contraction. [ABSTRACT FROM AUTHOR]

In this work a new method is developed to obtain C1-approximate solutions of initial and boundary-value problems generated from a one -- parameter second order singular ordinary differential equation. Information about the order of approximation is also given by introducing the so called growth index of a function. Conditions are given for the existence of such approximations for initial and boundary-value problems of several kinds. Examples associated with the corresponding graphs of the approximate solutions, for some values of the parameter, are also given. [ABSTRACT FROM AUTHOR]

Using the concept of majorant functions, we prove the existence and uniqueness of holomorphic solutions to nonlinear fractional diffusion problems. The analytic continuation of these solutions is studied and the singularity for two cases are posed. [ABSTRACT FROM AUTHOR]

This article is devoted to studying the solutions to the differential equation f(k) + Ak-1(z)f(k-1) + ⋯ + A0(z)f = 0, k ≥ 2, where coefficients Aj(z) are entire functions of integer order. We obtain estimates on the orders and the hyper orders of the solutions to the above equation. [ABSTRACT FROM AUTHOR]

We use a variation of Krasnoselskii fixed point theorem introduced by Burton to show that the nonlinear neutral differential equation x'(t) = -a(t)x³(t) + c(t)x'(t - g(t)) + G(t, x³(t - g(t)) has a periodic solution. Since this equation is nonlinear, the variation of parameters can not be applied directly; we add and subtract a linear term to transform the differential into an equivalent integral equation suitable for applying a fixed point theorem. Our result is illustrated with an example. [ABSTRACT FROM AUTHOR]

In this article, we establish necessary conditions for optimality in stochastic control of systems governed by stochastic differential equations with nonsmooth coefficients. The approach used is based on the approximation of the nonsmooth coefficient by smooth one which generate a sequence of smooth control problems. Ekeland's variational principle is then applied to obtain a sequence of nearly optimal controls which satisfy necessary conditions for near optimality. By using the generalized notion of Filippov's solutions and the stable convergence, we obtain an explicit formula for the adjoint process and the inequality between the Hamiltonians, on a good extension of the initial filtered probability space. [ABSTRACT FROM AUTHOR]

In this article we study elliptic systems called asymptotically homogeneous because their nonlinearities may not have polynomial growth. Using the Gidas-Spruck Blow-up method, we obtain a priori estimates, and then using Leray-Schauder topological degree theory, we obtain radial positive solutions vanishing at infinity. [ABSTRACT FROM AUTHOR]

In this article, we study the nonlinear dynamics of a quadratic system in the three dimensional space which can be obtained from a scalar third order differential equation. More precisely, we study the stability and bifurcations which occur in a parameter dependent quadratic system in the three dimensional space. We present an analytical study of codimension one, two and three Hopf bifurcations, generic Bogdanov-Takens and fold-Hopf bifurcations. [ABSTRACT FROM AUTHOR]

Using a fixed point theorem of strict-set-contraction, we prove the existence of positive periodic solutions for a class of nonautonomous impulsive neutral functional differential system with time-varying delays on time scales. [ABSTRACT FROM AUTHOR]

In this article we establish the existence of at least two distinct solutions to singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of sign-changing solutions for some second-order impulsive boundary-value problem with a sub-linear condition at infinity. To obtain the results we use the Leray-Schauder degree and the upper and lower solution method. [ABSTRACT FROM AUTHOR]

In this article, a fixed point theorem is used to investigate the existence of solutions for differential inclusions, with Neumann boundary conditions, in Banach spaces. [ABSTRACT FROM AUTHOR]

A method for finding solutions of the Riccati differential equation y' = P(x) + Q(x)y + R(x)y² is introduced. Provided that certain relations exist between the coefficient P(x), Q(x) and R(x), the above equation can be solved in closed form. We determine the required relations and find the general solutions to the aforementioned equation. The method is then applied to the Riccati equation arising in the solution of the multidimensional Gross-Pitaevskii equation of Bose-Einstein condensates by the F-expansion and the balance principle techniques. [ABSTRACT FROM AUTHOR]

In this article, we established the existence and uniqueness of solutions for fractional integro-differential equations with nonlocal conditions in Banach spaces. Krasnoselskii-Krein-type conditions are used for obtaining the main result. [ABSTRACT FROM AUTHOR]

We establish an oscillation criteria of the second-order nonlinear damped differential equation with functional arguments x"(t) + p(t)f(t, x(t), x'(t))x'(t) + q(t)g(x(t), x[h(t)]) = 0, t ∈ [t0, ∞). [ABSTRACT FROM AUTHOR]

In almost all papers in the literature, the results on exact controllability hold only for finite dimensional Banach spaces, since compactness of the semigroup and the bounded invertibility of an operator implies finite dimensional. In this note we show that the existence theory on controllability in the literature, can trivially be adjusted to include the infinite dimensional space setting, if we replace the compactness of operators with the complete continuity of the nonlinearity. [ABSTRACT FROM AUTHOR]

This paper concerns the existence of mild solutions for fractional semilinear differential equation with non local conditions in the α-norm. We prove existence and uniqueness, assuming that the linear part generates an analytic compact bounded semigroup, and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part. [ABSTRACT FROM AUTHOR]

In this article we study the fractional semilinear mixed Volterra-Fredholm integrodifferential equation Dαx(t)/dtα = Ax(t) + f(t, x(t), ∫t0t k(t, s, x(s))ds, ∫t0t h(t, s, x(s))ds), where t ∈ [t0, T], t0 ≥ 0, 0 < α < 1, and f is a given function. We prove the existence and uniqueness of solutions to this equation, with a nonlocal condition. [ABSTRACT FROM AUTHOR]