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http://dx.doi.org/10.14317/jami.2017.011

EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR SOME p(x)-LAPLACIAN-LIKE PROBLEMS VIA VARIATIONAL METHODS  

AFROUZI, G.A. (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran)
SHOKOOH, S. (Department of Mathematics, Faculty of Sciences, Gonbad Kavous University)
CHUNG, N.T. (Department of Mathematics, Quang Binh University)
Publication Information
Journal of applied mathematics & informatics / v.35, no.1_2, 2017 , pp. 11-24 More about this Journal
Abstract
Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.
Keywords
Variable exponent Sobolev spaces; Weak solutions; p(x)-Laplacian-like problems; Variational methods;
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