Abstract
In this paper, we establish the existence and multiplicity of symmetric positive solutions for a class of p-Laplacian fourth-order differential equations with integral boundary conditions. Our proofs use the Leray-Schauder nonlinear alternative and Krasnoselkii’s fixed-point theorem in cones.
Highlights
1 Introduction In this paper, we are concerned with the existence of symmetric positive solutions of the following fourth-order boundary-value problem with integral boundary conditions: φp u (t) = λw(t)f t, u(t), u (t), t ∈ (, ), ( . )
In [ ], Ma considered the existence of a symmetric positive solution for the fourthorder nonlocal boundary-value problem (BVP)
In Section, we use the Krasnoselkii fixed-point theorem to get the existence of multiple symmetric positive solutions for the nonlinear BVP ( . )-( . )
Summary
We are concerned with the existence of symmetric positive solutions of the following fourth-order boundary-value problem with integral boundary conditions: φp u (t) = λw(t)f t, u(t), u (t) , t ∈ ( , ),. In [ ], Zhang and Ge considered the existence and nonexistence of positive solutions of the following fourth-order boundary-value problems with integral boundary conditions:. In [ ], Ma considered the existence of a symmetric positive solution for the fourthorder nonlocal boundary-value problem (BVP). In Section , we use the Leray-Schauder nonlinear alternative to get the existence of at least one symmetric positive solution for the nonlinear BVP ). In Section , we use the Krasnoselkii fixed-point theorem to get the existence of multiple symmetric positive solutions for the nonlinear BVP To obtain the existence of symmetric positive solutions of the BVP
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