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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 2

Issues

Variational Approaches to P(X)-Laplacian-Like Problems with Neumann Condition Originated from a Capillary Phenomena

Shapour Heidarkhani / Ghasem A. Afrouzi / Shahin Moradi
Published Online: 2018-02-08 | DOI: https://doi.org/10.1515/ijnsns-2017-0114

Abstract

This article presents several sufficient conditions for the existence of at least one weak solution and infinitely many weak solutions for the following Neumann problem, originated from a capillary phenomena, {div((1+|u|p(x)1+|u|2p(x))|u|p(x)2u)+α(x)|u|p(x)2u=λf(x,u)inΩ,uν=0onΩ

where ΩRN (N2) is a bounded domain with boundary of class C1, ν is the outer unit normal to Ω, λ>0, αL(Ω), f:Ω×RR is an L1-Carathéodory function and pC0(Ω). Our technical approach is based on variational methods and we use a more precise version of Ricceri’s Variational Principle due to Bonanno and Molica Bisci. Some recent results are extended and improved. Some examples are presented to illustrate the application of our main results.

Keywords: variable exponent space; p(x)-Laplacian-likeproblem; weak solution; one solution; infinitely many solutions,variational methods

MSC 2010: Primary 35D05; Secondary 35J60

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About the article

Received: 2017-05-25

Accepted: 2018-01-15

Published Online: 2018-02-08

Published in Print: 2018-04-25


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 2, Pages 189–203, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0114.

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