Existence theory for nonlinear eigenvalue problems

Abstract

In this article, we study nonlinear boundary value problems of the form,

with boundary conditions

The λ we refer to is an eigenvalue of the associated linear Sturm–Liouville problem. We establish sufficient conditions for the existence of solutions to the nonlinear boundary value problem.

Keywords:

• boundary value problem; nonlinear
• fixed point theorem
• Schauder's theorem
• Liapunov–Schmidt