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Öğe Existence and multiplicity of the solutions of the p(x)-Kirchhoff type equation via genus theory(Wiley, 2011) Avcı, Mustafa; Çekiç, Bilal; Mashiyev, Rabil A.; 0000-0002-6001-627X; 0000-0002-6408-0455In this paper, by using variational approach and Krasnoselskii's genus theory, we show the existence and multiplicity of the solutions of the p(x)-Kirchhoff type equation.Öğe THE NEHARI MANIFOLD APPROACH FOR DIRICHLET PROBLEM INVOLVING THE p(x)-LAPLACIAN EQUATION(Korean Mathematical Soc, 2010) Mashiyev, Rabil A.; Ogras, Sezai; Yucedag, Zehra; Avci, MustafaIn this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.Öğe Nontrivial Solution for a Nonlocal Elliptic Transmission Problem in Variable Exponent Sobolev Spaces(Hindawi Ltd, 2010) Cekic, Bilal; Mashiyev, Rabil A.In this paper, by means of adequate variational techniques and the theory of the variable exponent Sobolev spaces, we show the existence of nontrivial solution for a transmission problem given by a system of two nonlinear elliptic equations of p(x)-Kirchhoff type with nonstandard growth condition.
