Yazar "Mashiyev, R. A." seçeneğine göre listele
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Öğe Existence and Localization Results for p(x)-Laplacian via Topological Methods(Hindawi Publishing Corporation, 2010) Cekic, B.; Mashiyev, R. A.We show the existence of a week solution in W(0)(1,p(x)) (Omega) to a Dirichlet problem for -Delta(p(x))u = f(x, u) in Omega, and its localization. This approach is based on the nonlinear alternative of Leray-Schauder.Öğe Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition(Taylor & Francis Ltd, 2012) Mashiyev, R. A.; Cekic, B.; Avci, M.; Yucedag, Z.We discuss the problem - div(a(x, del u)) = m(x)vertical bar u vertical bar(r(x)-2) u + n(x)vertical bar u vertical bar(s(x)-2)u in Omega, where Omega is a bounded domain with smooth boundary in R-N(N >= 2), and div(a(x, del u)) is a p(x)-Laplace type operator with 1 < r(x)< p(x)< s(x). We show the existence of infinitely many nontrivial weak solutions in W-0(1,p(x))(Omega). Our approach relies on the theory of the variable exponent Lebesgue and Sobolev spaces combined with adequate variational methods and a variation of the Mountain Pass lemma and critical point theory.Öğe Existence of solutions for a class of elliptic systems in RN involving the (p(x), q(x))-Laplacian(Springer, 2008) Ogras, S.; Mashiyev, R. A.; Avci, M.; Yucedag, Z.In view of variational approach, we discuss a nonlinear elliptic system involving the p(x)-Laplacian. Establishing the suitable conditions on the nonlinearity, we proved the existence of nontrivial solutions. Copyright (C) 2008 S. Ogras et al.Öğe Existence of solutions for p(x)-Laplacian equations(Univ Szeged, Bolyai Institute, 2010) Mashiyev, R. A.; Cekic, B.; Buhrii, O. M.We discuss the problem {-div (vertical bar Delta(u)vertical bar(p(x)-2)del(u))=lambda(a(x)vertical bar u vertical bar(q(x)-2) u + b(x)vertical bar u vertical bar(h(x)-2)u), for x is an element of Omega, u=0, for x is an element of partial derivative Omega. where Omega is a bounded domain with smooth boundary in R-N (N >= 2) and p is Lipschitz continuous, q and h are continuous functions on (Omega) over bar such that 1 < q(x) < p(x) < h(x) < p*(x) and p(x) < N. We show the existence of at least one nontrivial weak solution. Our approach relies on the variable exponent theory of Lebesgue and Sobolev spaces combined with adequate variational methods and the Mountain Pass Theorem.Öğe Existence of solutions of the parabolic variational inequality with variable exponent of nonlinearity(Academic Press Inc Elsevier Science, 2011) Mashiyev, R. A.; Buhrii, O. M.In this article, new properties of variable exponent Lebesgue and Sobolev spaces are examined. Using these properties we prove the existence of the solution of some parabolic variational inequality. (C) 2010 Elsevier Inc. All rights reserved.Öğe Hardy's inequality in power-type weighted LP(•) (0, ?) spaces(Academic Press Inc Elsevier Science, 2007) Mashiyev, R. A.; Cekic, B.; Mamedov, F. I.; Ogras, S.In this article, our aim is to prove Hardy's inequality in power-type weighted L-p(.) (0, infinity) spaces by obtaining regularity condition on the exponents p(.), q(.) and alpha(.) defined at every point of the domain of test function with u(0) = 0 (or vanishing at infinity) under the log-Holder continuity conditions at the origin and infinity. (c) 2006 Elsevier Inc. All rights reserved.Öğe Lp(x)(?)-estimates of vector fields and some applications to magnetostatics problems(Academic Press Inc Elsevier Science, 2012) Cekic, B.; Kalinin, A. V.; Mashiyev, R. A.; Avci, M.the present paper, we investigate Holder-type norm inequalities in terms of div and curl of the vector-valued functions in variable exponent Lebesgue spaces LP(x)(Omega), where Omega subset of R-3. Moreover, by using the obtained results we give some applications for magnetostatics problems. (C) 2011 Elsevier Inc. All rights reserved.Öğe Lyapunov, Opial and Beesack inequalities for one-dimensional p(t)-Laplacian equations(Elsevier Science Inc, 2010) Mashiyev, R. A.; Alisoy, G.; Ogras, S.We generalize the classical Lyapunov, Opial and Beesack inequalities for one-dimensional differential equations to nonstandard growth p(t)-Laplacian. (C) 2010 Elsevier Inc. All rights reserved.Öğe Solutions to semilinear p-Laplacian Dirichlet problem in population dynamics(Shanghai Univ, 2010) Mashiyev, R. A.; Alisoy, G.; Ogras, S.In this article, we study a semilinear p-Laplacian Dirichlet problem arising in population dynamics. We obtain the Morse critical groups at zero. The results show that the energy functional of the problem is trivial. As a consequence, the existence and bifurcation of the nontrivial solutions to the problem are established.Öğe Some properties of the first eigenvalue of the p(x)-laplacian on riemannian manifolds(Tubitak Scientific & Technological Research Council Turkey, 2009) Mashiyev, R. A.; Alisoy, G.; Ogras, S.The main results of the present paper establishes a stability property of the first eigenvalue of the associated problem which deals with the p(x)-Laplacian on Riemannian manifolds with Dirichlet boundary condition.Öğe Three Solutions to a Neumann Problem for Elliptic Equations with Variable Exponent(Springer Heidelberg, 2011) Mashiyev, R. A.In this article, we study the following nonlinear Neumann boundary value problem {(partial derivative u/partial derivative v) (-div(vertical bar del u vertical bar p(x)-2 del u) + a(x)vertical bar u vertical bar p(x)-2u = lambda f(x, u)) (on x is an element of partial derivative Omega) (in x is an element of Omega) where Omega subset of R-N (N >= 3), Omega is a bounded smooth domain and, p is an element of C ((Omega) over bar) with inf(x is an element of(Omega) over bar) p(x) > N, f : R -> R is a continuous function, and nu is the unit normal exterior vector on partial derivative Omega and a is an element of L-8(Omega), with ess infa(x) = a(0) > 0 and lambda > 0 is a real number. We first deal with the case that f (t) = b vertical bar t vertical bar(q-2)t - d vertical bar t vertical bar(s-2)t, t is an element of R, where b and d are positive constants. Then we deal with the case that f (x, t) = vertical bar t vertical bar(q(x)-2)t - vertical bar t vertical bar(s(x)-2)t, x is an element of Omega, t is an element of R, where q, s is an element of C ((Omega) over bar). Using the direct Ricceri variational principle, we establish the existence of at least three weak solutions of this problem in weighted-variable-exponent Sobolev space W-a(1,p(x)) (Omega).Öğe Uniqueness of solutions of the parabolic variational inequality with variable exponent of nonlinearity(Pergamon-Elsevier Science Ltd, 2009) Buhrii, O. M.; Mashiyev, R. A.in this article, new properties of variable exponent Lebesque and Sobolev spaces were examined. Using these properties we prove that the solution of some parabolic variational inequality is unique with the given conditions. (C) 2008 Elsevier Ltd. All rights reserved.
