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Öğe Electrorheological Fluids Equations Involving Variable Exponent with Dependence on the Gradient via Mountain Pass Techniques(Taylor and Francis Inc., 2016) Mashiyev R.A.; Ekincioglu I.This article deals with a quasilinear elliptic equation with variable exponent under a homogenous Dirichlet boundary-value condition, where nonlinearity also depends on the gradient of the solution. By using an iterative method based on Mountain Pass techniques, the existence of a positive solution is obtained. © 2016, Copyright © Taylor & Francis Group, LLC.Öğe Existence of one weak solution for p(X)-biharmonic equations involving a concave-convex nonlinearity(Drustvo Matematicara Srbije, 2017) Mashiyev R.A.; Alisoy G.; Ekincioglu I.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.Öğe Multiple small solutions for p(x)-Schrödinger equations with local sublinear nonlinearities via genus theory(University of Szeged, 2017) Ayazoglu Mashiyev R.; Ekincioglu I.; Alisoy G.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.
