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This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume as boundary conditions, periodic conditions in the horizontal directions, while in the vertical directions, slip-boundary is assumed for the velocity, vertical conditions for the magnetic field, and fixed temperature or fixed heat flux are prescribed for the temperature. The existence of stationary solution in a small neighborhood of a stationary profile close to hydrostatic state is obtained in Sobolev spaces as a fixed point of some nonlinear operator. [ABSTRACT FROM AUTHOR]

In this paper, we employ the well-known Krasnoselskii fixed point theorem to study the existence and n-multiplicity of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature. Easily verifiable sufficient criteria are obtained for the existence and n-multiplicity of positive periodic solutions of the impulsive functional differential equations. [ABSTRACT FROM AUTHOR]

This paper focuses on second-order differential equations involving causal operators with nonlinear two-point boundary conditions. By applying the monotone iterative technique in the presence of upper and lower solutions, with a new comparison theorem, we obtain the existence of extremal solutions. This is an extension of classical theory of second-order differential equations. Finally, we present two examples to show the usefulness of our results. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical analysis of a class of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator. We are concerned both with the coercive and the noncoercive (and nonresonant) cases, which are in relationship with two associated Rayleigh quotients. The proof combines critical point theory arguments and the dual variational principle. The arguments developed in this paper can be extended to other classes of nonlinear eigenvalue problems with nonstandard growth. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of concave and monotone positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form $x^{(4)}(t)=f(t,x(t),x'(t),x''(t))$, $t\in[0,1]$, $x(0)=x'(1)=x'''(1)=0$, $x''(0)=\int_{0}^{1}g(s)x''(s) \, \mathrm{d}s$, where $f\in C([0,1]\times[0,+\infty)^{2}\times(-\infty,0],[0,+\infty))$, $g\in C([0,1],[0,+\infty))$. By using a fixed point theorem of cone expansion and compression of norm type, the existence and nonexistence of concave and monotone positive solutions for the above boundary value problems is obtained. Meanwhile, as applications of our results, some examples are given. [ABSTRACT FROM AUTHOR]

Motivated by (Kyoung and Yong-Hoon in Sci. China Math. 53:967-984, 2010) and (Chen and Zhang in Sci. China Math. 54:959-972, 2011), this paper is concerned with a boundary value problem of singular second-order differential systems with quasi-Laplacian operators on the whole line. By constructing a completely continuous nonlinear operator and using a fixed point theorem, sufficient conditions guaranteeing the existence of at least one unbounded solution are established. The methods used are standard, however, their exposition in the framework of such a kind of problems is new and skillful. Three concrete examples are given to illustrate the main theorem. [ABSTRACT FROM AUTHOR]

In this paper, we consider a one-dimensional mean curvature equation in Minkowski space and the corresponding one-parameter problem. By using a fixed point theorem of cone expansion and compression of norm type, the existence and multiplicity of positive solutions for the above problems are obtained. Meanwhile, as applications of our results, some examples are given. [ABSTRACT FROM AUTHOR]

The paper deals with the existence and non-existence of solutions of the following nonlinear non-autonomous boundary value problem governed by the p-Laplacian operator: (P) { (h (t , x (t)) | x ′ (t) | p − 2 x ′ (t)) ′ = g (t , x (t) , x ′ (t)) a.e. t ∈ R , x (− ∞) = a , x (+ ∞) = b with a < b , where a is a positive, continuous function and g is a Caratheódory nonlinear function. We prove an existence result, underlying the relationship between the behavior of g (t , x , ⋅) as y → 0 related to that of g (⋅ , x , y) and h (⋅ , x) as | t | → + ∞ . [ABSTRACT FROM AUTHOR]

In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin–Voigt model. At the same time, the corresponding eigenvalue problem is studied and the property of solution for the eigenvalue problem is established. Some examples are given to illuminate the main results. [ABSTRACT FROM AUTHOR]

In this paper, by studying the solutions of the abstract operator equation A(x,x)+B(x,x)+e=x on ordered Banach spaces, where A, B are two mixed monotone operators and e∈P with θ≤e≤h, we prove a class of boundary value problems on elastic beam equation to have a unique solution. Furthermore, we also apply our abstract result to establish the existence and uniqueness theorem of nontrivial solutions for nonlinear fractional boundary value problems. The iterative sequences to approximate unique solutions for the above two classes of problems are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of positive solutions of fractional differential equations on the infinite interval (0,+∞). The positive solution of fractional differential equations is gained by using the properties of the Green’s function, Leray-Schauder’s fixed point theorems, and Guo-Krasnosel’skii’s fixed point theorem. As an application, two examples are given to prove our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the fixed point for a class of nonlinear sum-type operators ‘A+B+C’ on an ordered Banach space, where A, B are two mixed monotone operators, C is an increasing operator. Without assuming the existence of upper-lower solutions or compactness or continuity conditions, we prove the unique existence of a positive fixed point and also construct two iterative schemes to approximate it. As applications, we research a nonlinear fractional differential equation with multi-point fractional boundary conditions. By using the obtained fixed point theorems of sum-type operator, we get the sufficient conditions which guarantee the existence and uniqueness of positive solutions. At last, a specific example is provided to illustrate our result. [ABSTRACT FROM AUTHOR]

In this paper, we study the multiplicity of periodic solutions of one kind of planar Hamiltonian systems with a nonlinear term satisfying semilinear conditions. Using a generalized Poincaré-Birkhoff fixed point theorem, we prove that the system has infinitely many periodic solutions, provided that the time map tends to zero. [ABSTRACT FROM AUTHOR]

Here, a nonlocal nonlinear operator known as the fractional (p , q) -Laplacian is considered. The existence of a mountain pass solution is proved via critical point theory and variational methods. To this aim, the well-known theorem on the construction of the critical set of functionals with a weak compactness condition is applied. [ABSTRACT FROM AUTHOR]

Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations {x¨+a(t)x=f(x),x(0)=x(T),x˙(0)=x˙(T). For given nonnegative constants 0<β1<β2<⋯<βN, the function f may be singular at x=βi. [ABSTRACT FROM AUTHOR]

In this article, we first of all convert the boundary value problems for impulsive fractional differential equations to integral equations. Second, we construct a weighted function space and prove the completely continuous property of a nonlinear operator. Finally, we establish existence results for solutions of a boundary value problem for a nonlinear impulsive fractional differential system. Our analysis relies on the well-known Schauder fixed point theorem. An example is given to illustrate main results. [ABSTRACT FROM AUTHOR]

Given a bounded open regular set Ω ∈ R 4 , x 1 , x 2 , ... , x m ∈ Ω , λ , ρ > 0 , γ ∈ (0 , 1) , and Q λ some nonlinear operator (which will be defined later), we prove that the problem Δ 2 u + Q λ (u) = ρ 4 (e u + e γ u) has a positive weak solution in Ω with u = Δ u = 0 on ∂Ω, which is singular at each x i as the parameters λ and ρ tend to 0. [ABSTRACT FROM AUTHOR]

We study the following system of equations: 0.1 { Δ u 1 = p 1 (| x |) f 1 (u 1 , u 2) in R N , Δ u 2 = p 2 (| x |) f 2 (u 1 , u 2) in R N. Here f 1 , f 2 are continuous nonlinear functions that satisfy Keller–Osserman-type conditions, and p 1 and p 2 are continuous weight functions. We establish the existence of radial solutions for this system under various boundary conditions. [ABSTRACT FROM AUTHOR]