Nontrivial solutions for semilinear elliptic systems via Orlicz–Sobolev theory. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Fang, Fei; Ji, Chao
• Is Part Of: Complex variables and elliptic equations. Volume 61:Issue 4(2016)
• Page Start: 524
• Page End: 537
• Publication Date: 2016-04-02
• Subjects: Semilinear elliptic systems -- Orlicz–Sobolev space -- concentration-compactness principle; 35J20 -- 35J65 -- 35J70 -- 58E05; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2015.1106480
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : In this paper, the semilinear elliptic systems with Dirichlet boundary value are considered We extend the notion of subcritical growth from polynomial growth to N-function growth. Under N-function growth, nontrivial solutions are obtained via Orlicz–Sobolev space theory and variational method. It is also noteworthy that the nonlinear term g ( v ) does not have to satisfy the usual Ambrosetti–Rabinowitz condition. So, in some sense, we enrich recent results of D.G. de Figueiredo, J.M. doÓ and B. Ruf [de Figueiredo DG, doÓ JM, Ruf B, An Orlicz-space approach to superlinear elliptic systems, J. Funct. Anal. 2005;224:471–496].