Ayazoglu, Rabil; Alisoy, Gulizar; Akbulut, Sezgin; Aydin, Tuba Agirman

In 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.

AtıfScopus1·WoS1·OpenAlex1

İncele

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.

AtıfScopus2·WoS1·OpenAlex2

İncele

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.

AtıfScopus7·WoS7·OpenAlex4

İncele