Resonant (p,q)-equations with Robin boundary condition

Abstract

We consider a nonlinear nonhomogeneous Robin problem that has the sum of a p-Laplacian and a q-Laplacian (a (p,q)-equation). The reaction term is a Caratheodory function which is resonant at $\pm\infty$ with respect to any nonprincipal variational eigenvalue of the Robin p-Laplacian. Using variational methods and Morse theory (critical groups), we show the existence of at least three nontrivial smooth solutions.

Keywords

• (p,q)-Laplace differential operator
• resonance
• critical groups
• multiple solutions
• nonlinear regularity