Existence results for Schrödinger type double phase variable exponent problems with convection term in $ \mathbb R^{N} $

Abstract

This paper was concerned with a new class of Schrödinger equations involving double phase operators with variable exponent in $ \mathbb R^{N} $. We gave the corresponding Musielak-Orlicz Sobolev spaces and proved certain properties of the double phase operator. Moreover, our main tools were the topological degree theory and Galerkin method, since the equation contained a convection term. By using these methods, we derived the existence of weak solution for the above problems. Our result extended some recent work in the literature.

Keywords

• variable exponent
• double phase problem
• convection term
• galerkin method
• topological degree