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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(2009) Mashiyev, R. A.; Alisoy, G.; Ogras, S.Abstract: The main result 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.
