一类非齐次Schrodinger-Poisson系统解的存在性

Existence of solutions for a class of inhomogeneous Schrodinger-Poisson system

研究一类非齐次Schrodinger-Poisson系统{-△u+V(x)u+φ(x)u=f(u)+g(x),x∈R^(3)-△φ=u^(2),x∈R^(3)。当V(x)为径向对称位势,非齐次扰动项g(x)的范数足够小时,通过Ekeland’s变分原理和结合单调性方法的山路定理,证明了该系统解的存在性;当V(x)为强制位势且f(u)为奇函数时,通过(sP.S)_(c)条件和对称山路引理构造一趋于无穷大的临界值序列,获得系统无穷多解的存在性。

In this paper,we are concerned with a class of inhomogeneous Schrodinger-Poisson systems{-△u+V(x)u+φ(x)u=f(u)+g(x),x∈R^(3)-△φ=u^(2),x∈R^(3).When V(x)is a radially symmetric potential and the norm of the inhomogeneous term g(x)is sufficiently small,we prove the existence of the solutions of the system via Ekeland’s variational principle and the mountain pass lemma combined with a monotonicity method.When V(x)is a coercive potential and f(u)is an odd function,by using the(sP.S)c condition and symmetric mountain pass theorem,we construct a sequence of critical values that tends to infinity,and thus confirm the existence of infinitely many solutions of the equation.