Existence of positive solutions of Kirchhoff hyperbolic systems with multiple parameters

In this paper, by using sub-super solutions method, we study the existence of weak positive solution of Kirrchoff hyperbolic systems in bounded domains with multiple parameters. These results extend and improve many results in the literature

Existence of positive solutions of Hadamard fractional defferential equations with integral boundary conditions

In this paper, We study the existence of positive solutions for Hadamard fractional differential equations with integral conditions. We employ Avery-Peterson fixed point theorem and properties of Green's function to show the existence of positive solutions of our problem. Furthermore, we present an example to illustrate our main result.

Existence of positive solutions for a class of BVPs in Banach spaces

In this work, we use index xed point theory for perturbation of expan- sive mappings by l-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear di erential equation on the positive half-line. The nonlin- earity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave di erently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main results is given.

Quasilinear Choquard equations involving N-Laplacian and critical exponential nonlinearity

In the present paper, we study a class of quasilinear Choquard equations involving N-Laplacian and the nonlinearity with the critical exponential growth. We discuss the existence of positive solutions of such equations.

Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives

This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.

On positive solutions of second-order delayed differential system with indefinite weight

In this paper, we study the existence of positive solutions of a second-order delayed differential system, in which the weight functions may change sign. To prove our main results, we apply Krasnosel’skii’s fixed point theorems in cones.

Existence of positive solutions for a system of nonlinear Caputo type fractional differential equations with two parameters

The main purpose of this paper is to prove the existence of positive solutions for a system of nonlinear Caputo-type fractional differential equations with two parameters. By using the Guo–Krasnosel’skii fixed point theorem, some existence theorems of positive solutions are obtained in terms of different values of parameters. Two examples are given to illustrate the main results.

Existence of Solutions to a Class of Nonlinear Arbitrary Order Differential Equations Subject to Integral Boundary Conditions

We investigate the existence of positive solutions for a class of fractional differential equations of arbitrary order δ>2, subject to boundary conditions that include an integral operator of the fractional type. The consideration of this type of boundary conditions allows us to consider heterogeneity on the dependence specified by the restriction added to the equation as a relevant issue for applications. An existence result is obtained for the sublinear and superlinear case by using the Guo–Krasnosel’skii fixed point theorem through the definition of adequate conical shells that allow us to localize the solution. As additional tools in our procedure, we obtain the explicit expression of Green’s function associated to an auxiliary linear fractional boundary value problem, and we study some of its properties, such as the sign and some useful upper and lower estimates. Finally, an example is given to illustrate the results.

Existence of Positive Solution for a Singular Fourth–Order Differential System

This paper investigates the existence of positive solutions for a fourth-order differential system using a fixed point theorem of cone expansion and compression type.