On the Positive Solutions of a Nonlinear Fourth-order Boundary Value Problem with Two Parameters

Abstract

The existence of m positive solutions is proven for a nonlinear fourth-order boundary value problem with two parameters, where m is an arbitrary natural number. This kind of fourth-order boundary value problems usually describes the equilibrium state of elastic beam where both ends are simply supported. The main ingredient is Krasnosel'skii fixed point theorem of cone expansion–compression type.

Keywords:

• Nonlinear fourth-order boundary value problem
• Positive solution
• Existence
• Multiplicity
• Nonexistence