Multiple solutions for some elliptic boundary value problem with jumping nonlinearities

Abstract

We investigate the multiplicity of solutions for the one-dimensional elliptic Dirichlet boundary value problem with jumping nonlinearities. We obtain three theorems depending on the source terms when nonlinearities cross some eigenvalues. We obtain the first theorem and the second one by eigenvalues and the corresponding normalized eigenfunctions of the elliptic eigenvalue problem, and the contraction mapping principle on p-Lebesgue space. We obtain the third result by Leray–Schauder degree theory.