Multiple positive solutions to a fourth-order boundary-value problem

Abstract

We study the existence, localization and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem, and unilateral Harnack type inequalities.

Keywords

• Fourth-order differential equation
• boundary-value problem
• positive solution
• critical point
• fixed point