Positive periodic solutions of nonlinear differential equations system with nonstandard growth

In this work, we study the existence of positive periodic solutions for a p(t)-Laplacian system. © 2014 Elsevier Ltd

Infinitely many solutions for a class of stationary Schrödinger equations with non-standard growth

In this paper, we study the existence of infinitely many solutions for a class of stationary Schrödinger type equations in ?N involving the p(x)-Laplacian. The non-linearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. The main arguments are based on the geometry supplied by Fountain Theorem. We also establish a Bartsch type compact embedding theorem for variable exponent spaces. © 2017 Informa UK Limited, trading as Taylor & Francis Group

Multiple small solutions for p(x)-Schrödinger equations with local sublinear nonlinearities via genus theory

In this paper, we deal with the following p(x)-Schrödinger problem: (Formula Presented) where the nonlinearity is sublinear. We present the existence of infinitely many solutions for the problem. The main tool used here is a variational method and Krasnoselskii’s genus theory combined with the theory of variable exponent Sobolev spaces. We also establish a Bartsch-Wang type compact embedding theorem for the variable exponent spaces. © 2017, University of Szeged. All rights reserved