Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian
Pure and Applied Mathematics Journal
Volume 2, Issue 1, February 2013, Pages: 20-27
Received: Jan. 14, 2013; Published: Feb. 20, 2013
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Mustafa Avci, Department of Mathematics, Dicle University, Diyarbakir, Turkey
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In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.
p(x)-Laplacian; Nonlocal Problem; Fixed Point Theorem; Galerkin Method; Variational Methods Moun-tain-Pass Theorem
To cite this article
Mustafa Avci, Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian, Pure and Applied Mathematics Journal. Vol. 2, No. 1, 2013, pp. 20-27. doi: 10.11648/j.pamj.20130201.13
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