变号位势哈密顿椭圆系统解的存在性

Existence of solution for Hamiltonian elliptic systems with signchanging potential

考虑以下具有变号位势的非周期超二次哈密顿椭圆系统{-△u+b(x)·▽u+V(x)u=H_v(x,u,v),-△v-b(x)·▽u+V(x)v=H_u(x,u,v),x∈R^N u(x),v(x)→0,|x|→∞其中z=(u,v):R^N→R×R,当|z|→∞时,H(x,z)关于z是超二次的,在位势V变号的假设下,利用强不定泛函的临界点理论证明此系统存在一个非平凡解。

Using a critical point theorem for strongly indefinite functions, the existence of solution is obtained for the following Hamihonian elliptic systems.{-△u＋b（x）·▽u＋V（x）u=H_v（x,u,v）,-△v-b（x）·▽u＋V（x）v=H_u（x,u,v）,x∈R^N u（x）,v（x）→0,｜x｜→∞where z =（u,v）：R^N→R×R,H（x,z）is superquadratic and nonperiodic and the potential V is nonperiodic and maybe signchanging.