Nontrivial solutions for semilinear elliptic systems via Orlicz–Sobolev theory. Issue 4 (2nd April 2016) - Fang, Fei; Ji, Chao
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].