摘要
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.
作者
蔡武晋
边慎
赵雷嘎
CAI WuJin;BIAN Shen;ZHAO LeiGa(College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029;School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China)
出处
《北京化工大学学报(自然科学版)》
CAS
CSCD
北大核心
2021年第4期119-124,共6页
Journal of Beijing University of Chemical Technology(Natural Science Edition)
基金
北京工商大学科研启动费(19008020161)。