Existence and multiplicity of solutions for a quasilinear equation involving the p(x)-Laplace operator. Issue 3 (4th March 2017)

• Record Type: Journal Article
• Authors: Saoudi, K.
• Is Part Of: Complex variables and elliptic equations. Volume 62:Issue 3(2017)
• Page Start: 318
• Page End: 332
• Publication Date: 2017-03-04
• Subjects: p(x)-Laplace operator -- quasilinear equation -- variational methods -- generalized Lebesgue Sobolev spaces; 35J20 -- 35J60 -- 35J70 -- 47J10 -- 46E35; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2016.1219999
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : The purpose of this paper is to study the following nonlinear problem involving the p ( x )-Laplace operator: where is a bounded domain with boundary, is a positive parameter, p ( x ), and f ( x, u ) are assumed to satisfy the assumptions(H1) –(H4) in the introduction. We employ variational techniques in order to show the existence of a number such that problem admits two solutions for one solution for and no solutions for