Yujun Cui

Uniqueness and Existence of Positive Solutions for Singular Differential Systems with Coupled Integral Boundary Value Problems

This paper provides sufficient conditions for the existence and uniqueness of positive solutions to a singular differential system with integral boundary value. The emphasis here is that the boundary conditions are coupled and this is where the main novelty of this work lies. By mixed monotone method, the existence and uniqueness results of the problem are established. An example is given to demonstrate the main results.

Existence of multiple positive solutions for fourth-order boundary value problems in Banach spaces

This paper deals with the positive solutions of a fourth-order boundary value problem in Banach spaces. By using the fixed-point theorem of strict-set-contractions, some sufficient conditions for the existence of at least one or two positive solutions to a fourth-order boundary value problem in Banach spaces are obtained. An example illustrating the main results is given.MSC:34B15.

Positive Solutions for Fourth-Order Singular -Laplacian Differential Equations with Integral Boundary Conditions

By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo- as well as positive solutions for fourth-order singular -Laplacian differential equations with integral boundary conditions. Our nonlinearity may be singular at , , and . The dual results for the other integral boundary condition are also given.

Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory

This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: , , where , with , and stand for the left and right Riemann-Liouville fractional derivatives of order , respectively, and is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.