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Existence of one weak solution for p(X)-biharmonic equations involving a concave-convex nonlinearity
(Drustvo Matematicara Srbije, 2017) Mashiyev, R.A.; Alisoy, Gülizar; Ekincioğlu, İsmail
In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involving a p(x)-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditions is obtained. © 2017, Drustvo Matematicara Srbije. All rights reserved.
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.