Infinitely Many Small Energy Solutions to the Double Phase Anisotropic Variational Problems Involving Variable Exponent

Abstract

This paper is devoted to double phase anisotropic variational problems for the case of a combined effect of concave–convex nonlinearities when the convex term does not require the Ambrosetti–Rabinowitz condition. The aim of the present paper, on a class of superlinear term which is different from the previous related works, is to discuss the multiplicity result of non-trivial solutions by applying the dual fountain theorem as the main tool. In particular, our main result is obtained without assuming the conditions on the nonlinear term at infinity.

Keywords

• double phase equations
• variable exponent Orlicz-Sobolev spaces
• variational methods
• multiple solutions