Existence and concentration properties of ground state solutions for elliptic systems

Abstract

ABSTRACTThis article is concerned with following Hamiltonian elliptic system with gradient term: where ϵ is a small positive parameter, b is a constant vector, , V is allowed to be sign-changing and . Using a much more direct approach, we study above system and prove first the existence of ground state solutions for each , is a constant which depends on N,V,Q and F. We consider further the exponential decay and concentration phenomena of ground states for the system. Particularly, we show that these ground states concentrate around a global minimum point of the linear potential V or a global maximum point of the nonlinear potential Q as .