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- MakaleYalnız künye2018Scopus SJRQ2Infinitely many solutions for a class of stationary Schrödinger equations with non-standard growth
Ayazoglu (Mashiyev), R.; Alisoy, Gulizar
In this paper, we study the existence of infinitely many solutions for a class of stationary Schrödinger type equations in ℝN 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.
AtıfScopus2WoS1OpenAlex2
İncele - MakaleAçık Erişim2017Scopus SJRQ3Multiple small solutions for p(x)-Schrödinger equations with local sublinear nonlinearities via genus theory
Ayazoglu Mashiyev, Rabil; Ekincioglu, Ismail; Alisoy, Gulizar
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.
AtıfScopus7WoS7OpenAlex4İncele - MakaleAçık Erişim2013Scopus SJRQ3Existence of solutions for an elliptic equation with nonstandard growth
Avci, M.; Mashiyev, R. Ayazoglu; Cekic, B.
This paper deals with the existence of solutions for some elliptic equations with nonstandard growth under zero Dirichlet boundary condition. Using a direct variational method and the theory of the variable exponent Sobolev spaces, we set some conditions that ensures the existence of nontrivial weak solutions.
AtıfScopus2OpenAlex2İncele