EXISTENCE OF GROUND STATE SOLUTIONS TO HAMILTONIAN ELLIPTIC SYSTEM WITH POTENTIALS

摘要

In this paper,we investigate nonlinear Hamiltonian elliptic system ｛-△u + (b)(x)·▽u + (V(x) + τ)u =K(x)g(v) in RN,-△v-(b)(x)· ▽v + (V(x) + τ)v =K(x)f(u) in RN,u(x)→ 0 and v(x) → 0 as ｜x｜→∞,where N ≥ 3,τ ＞ 0 is a positive parameter and V,K are nonnegative continuous functions,f and g are both superlinear at 0 with a quasicritical growth at infinity.By establishing a variational setting,the existence of ground state solutions is obtained.