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

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Ayazoğlu, Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir

This paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.) - Kirchhoff-type equation (Formula Presented). Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of the variable exponent Sobolev spaces, under appropriate assumptions on f and M, we obtain results on existence and multiplicity of solutions

AtıfScopus9·WoS9·OpenAlex9

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Ayazoglu, Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir

In this paper, we prove the existence of multiple solutions for the nonhomogeneous Schrödinger-Kirchhoff-type problem involving the p(.)-Laplacian (Formula presented.) where b≥0 is a constant, N ≥2, Δp(.)u:=div(|∇u|p(.)−2∇u) is the p(.)-Laplacian operator, (Formula presented.) is Lipschitz continuous, (Formula presented.) is a coercive type potential, (Formula presented.) and (Formula presented.) functions verifying suitable conditions. We propose different assumptions on the nonlinear term (Formula presented.) to yield bounded Palais-Smale sequences and then prove that the special sequences we found converge to critical points, respectively. The solutions are obtained by the Mountain Pass Theorem, Ekeland variational principle, and Krasnoselskii genus theory.

AtıfScopus1·WoS1

İncele

Ayazoglu, Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir

In this paper, the Kantorovich operators Kn, n ϵ N are shown to be uniformly bounded in variable exponent Lebesgue spaces on the closed interval [0, 1]. Also an upper estimate is obtained for the difference Kn (f) − f for functions f of regularity of order 1 and 2 measured in variable exponent Lebesgue spaces, which is of interest on its own and can be applied to other problems related to the Kantorovich operators.

AtıfScopus3·WoS3·OpenAlex3

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