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Öğe Existence and extinction of solutions for parabolic equations with nonstandard growth nonlinearity(Hacettepe Univ, Fac Sci, 2024) Ayazoglu (Mashiyev), Rabil; Alisoy, Gulizar; Akbulut, Sezgin; Aydin, Tuba AgirmanIn this paper, we consider an initial boundary value problem for a class of p ( ) -Laplacian parabolic equation with nonstandard nonlinearity in a bounded domain. By using new approach, we obtain the global and decay of existence of the solutions. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.Öğe Existence and multiplicity of solutions for a Schrodinger-Kirchhoff type equation involving the fractional p(.,.)-Laplacian operator in RN(Springer-Verlag Italia Srl, 2021) Ayazoglu, Rabil; Sarac, Yesim; Sener, S. Sule; Alisoy, GulizarIn this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii's genus theory, we show the existence and multiplicity of solutions for a Schrodinger-Kirchhoff type equation involving the fractional p-Laplacian in fractional Sobolev space with variable exponent. We also establish a Bartsch-Wang type compact embedding theorem for fractional Sobolev space with variable exponent.Öğe EXISTENCE OF ONE WEAK SOLUTION FOR p(x)-BIHARMONIC EQUATIONS INVOLVING A CONCAVE-CONVEX NONLINEARITY(Math Soc Serbia-Drustvo Matematicara Srbije, 2017) Ayazoglu (Mashiyev), Rabil; Alisoy, Gulizar; Ekincioglu, IsmailIn 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 involvinga p(x)-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditionsis obtained.
