Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions
Volume 104 / 2012
Annales Polonici Mathematici 104 (2012), 293-308
MSC: Primary 35J25; Secondary 35J60.
DOI: 10.4064/ap104-3-6
Abstract
Our main purpose is to establish the existence of a positive solution of the system where \Omega\subset {\mathbb R}^N is a bounded domain with C^2 boundary, F(x,u,v)=\lambda^{p(x)}[g(x)a(u)+f(v)], H(x,u,v)=\lambda^{q(x)} [g(x)b(v)+h(u)], \lambda>0 is a parameter, p(x), q(x) are functions which satisfy some conditions, and -\triangle_{p(x)}u=-\mbox{div}(|\nabla u|^{p(x)-2}\nabla u) is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.
