Fractional N-Laplacian boundary value problems with jumping nonlinearities in the fractional Orlicz–Sobolev spaces

Abstract

Abstract We investigate the multiplicity of solutions for problems involving the fractional N-Laplacian. We obtain three theorems depending on the source terms in which the nonlinearities cross some eigenvalues. We obtain these results by direct computations with the eigenvalues and the corresponding eigenfunctions for the fractional N-Laplacian eigenvalue problem in the fractional Orlicz–Sobolev spaces, the contraction mapping principle on the fractional Orlicz–Sobolev spaces and Leray–Schauder degree theory.

Keywords

• Fractional N-Laplacian operator
• Fractional Orlicz–Sobolev space
• Fractional N-Laplacian eigenvalue problem
• Jumping nonlinearity
• Contraction mapping principle
• Leray–Schauder degree theory