A multiplicity theorem for parametric superlinear (p,q)-equations

Abstract

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

Keywords

• superlinear reaction
• constant sign and nodal solutions
• extremal solutions
• nonlinear regularity
• nonlinear maximum principle
• critical groups