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- MakaleAçık Erişim2022Scopus SJRQ2Existence and multiplicity of solutions for p(.)-Kirchhoff-type equations
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
AtıfScopus9WoS9OpenAlex9
İncele - MakaleAçık Erişim2021Scopus SJRQ1Existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional p(. ,.) -Laplacian operator in RN
Ayazoglu, Rabil; Saraç, Yeşim; Şener, S. Şule; Alisoy, Gülizar
In this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii’s genus theory, we show the existence and multiplicity of solutions for a Schrödinger–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.
AtıfScopus21WoS22OpenAlex22İncele - MakaleAçık Erişim2020Scopus SJRQ1Existence of multiple solutions of Schrödinger-Kirchhoff-type equations involving the p(.) -Laplacian in ℝN
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.
AtıfScopus1WoS1İncele - MakaleYalnız künye2017Scopus SJRQ2Existence of one weak solution for p(X)-biharmonic equations involving a concave-convex nonlinearity
Mashiyev, Rabil Ayazoglu; Alisoy, Gülizar; Ekincioglu, Ismail
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.
AtıfScopus10İncele - MakaleAçık Erişim2016Scopus SJRQ1Electrorheological Fluids Equations Involving Variable Exponent with Dependence on the Gradient via Mountain Pass Techniques
Mashiyev, R. Ayazoglu; Ekincioglu, Ismail
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.
AtıfScopus11WoS10OpenAlex13İncele - MakaleAçık Erişim2013Scopus SJRQ1Solutions of an anisotropic nonlocal problem involving variable exponent
Avci, Mustafa; Ayazoglu, Rabil A.; Cekic, Bilal
The present paper deals with an anisotropic Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of ℝN (N ≥ 3). The problem studied is a stationary version of the original Kirchhoff equation, involving the anisotropic p→(.)-Laplacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Applying the Mountain Pass Theorem of Ambrosetti and Rabinowitz, the existence of a nontrivial weak solution is obtained in the anisotropic variable exponent Sobolev space W01p→(.) (Ω), provided that the positive parameter λ that multiplies the nonlinearity f is small enough.
AtıfScopus13WoS14OpenAlex9İncele - MakaleAçık Erişim2013Scopus SJRQ3Existence of solutions for an elliptic equation with nonstandard growth
Avci, M.; Mashiyev, R. Ayazoglu; Cekic, B.
This paper deals with the existence of solutions for some elliptic equations with nonstandard growth under zero Dirichlet boundary condition. Using a direct variational method and the theory of the variable exponent Sobolev spaces, we set some conditions that ensures the existence of nontrivial weak solutions.
AtıfScopus2OpenAlex2İncele