Anisotropic $ (\vec{p}, \vec{q}) $-Laplacian problems with superlinear nonlinearities

Abstract

In this paper we consider a class of anisotropic $ (\vec{p}, \vec{q}) $-Laplacian problems with nonlinear right-hand sides that are superlinear at $ \pm\infty $. We prove the existence of two nontrivial weak solutions to this kind of problem by applying an abstract critical point theorem under very general assumptions on the data without supposing the Ambrosetti-Rabinowitz condition.

Keywords

• anisotropic problems
• critical point theory
• existence
• multiplicity results
• location of the solutions
• parametric problem
• $ (\vec{p}， \vec{q}) $-laplacian
• superlinear nonlinearity