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Infinitely many solutions for a class of stationary Schrodinger equations with non-standard growth
(Taylor & Francis Ltd, 2018) Ayazoğlu (Mashiyev), Rabil; Alisoy, Gülizar
In this paper, we study the existence of infinitely many solutions for a class of stationary Schrodinger type equations in R-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.
Multiple small solutions for p(x)-Schrodinger equations with local sublinear nonlinearities via genus theory
(Univ Szeged, Bolyai Institute, 2017) Ayazoğlu (Mashiyev), Rabil; Ekincioğlu, İsmail; Alisoy, Gülizar
In this paper, we deal with the following p(x) - Schrodinger problem: { (-div (vertical bar del u vertical bar(p(x)-2)del u) + V(x) vertical bar u vertical bar(p(x)-2) u = f (x, u) in R-N; u is an element of W-1,W-p(x) (R-N), 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.