Yazar "Akbulut, Sezgin" seçeneğine göre listele

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    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 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.
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    Existence and multiplicity of solutions for p(.)-Kirchhoff-type equations
    (Tubitak Scientific & Technological Research Council Turkey, 2022) AyazoClu, 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 {M(integral(Omega)vertical bar del vertical bar p(x)/p(x)dx) (-Delta(p(x))u) = f(x,u), in Omega, u = 0, on partial derivative Omega 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.
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    Existence of multiple solutions of Schrodinger-Kirchhoff-type equations involving the p(.) -Laplacian in RN
    (Wiley, 2020) Ayazoglu (Mashiyev), Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir
    In this paper, we prove the existence of multiple solutions for the nonhomogeneous Schrodinger-Kirchhoff-type problem involving the p(.)-Laplacian {-(1+b integral(N)(R)1/p(x)vertical bar del u vertical bar(p(x)) dx) Delta(p(x))u+V(x)vertical bar u vertical bar p((x)-2) u=f(x,u) + g(x) in R-N, u is an element of W-1,W-p(.)(R-N), where b >= 0 is a constant, N >= 2, Delta(p)(.)u := div(vertical bar del u vertical bar p((.)-2)del u) is the p(.)-Laplacian operator, p : R-N -> R is Lipschitz continuous, V : R-N -> R is a coercive type potential, integral : R-N x R -> R and g : R-N -> R functions verifying suitable conditions. We propose different assumptions on the nonlinear term f : R-N x R -> R 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.
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    THE APPLICATIONS IN ENGINEERING OF EQUATIONS WITH NON-STANDARD GROWTH CONDITIONAL
    (E-Journal of New World Sciences Academy, 2018) Akkoyunlu, Ebubekir; Ayazoğlu, Rabil; Akbulut, Sezgin
    Many materials and problems in physics and engineering applications can be mathematically modeled with sufficient accuracy using classical Lebesgue and classical Sobolev spaces. However, must be variable in order to be expressed correctly the underlying energy of some nonhomogeneous materials. Such problems can be solved only in the variable-exponent Lebesgue and Sobolev spaces. Therefore, in recent years, the interest to partial differential equations with non-standard growth conditional involving -Laplacian (with growth conditional) and variational integrals have been increased. Electrorheological Fluids Theory, Nonlinear Elasticity Theory, Image Processing, Flow in Porous Media are some of the application areas in engineering of non-standard growth conditional differential equations involving -Laplacian. Especially Electrorheological fluids have been used in robotics and space technology (The Research is mostly done in America and especially in NASA laboratories) have significiant importance. In this presentation, we provide information on variational integrals and on nonstandard growth-conditional partial differential equations involving -Laplacian, which has an important role in applied sciences (especially in engineering).
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    Uniform Boundedness of Kantorovich Operators in Variable Exponent Lebesgue Spaces
    (Univ Nis, Fac Sci Math, 2019) Ayazoglu (Mashiyev), Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir
    In this paper, the Kantorovich operators K-n, n is an element of 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 K-n(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.