摘要
该文研究如下Schrdinger-Poisson系统解的存在性和多重性-△u+V(x)u+K(x)φu=f(x,u),x∈R^3,-△φ=K(x)u^2,x∈R^3,其中V∈C(R^3,R)并且K∈L^2∪L~∞满足K>0.在没有Ambrosetti-Rabinowitz型超二次条件以及映射t→(f(x,t))/t^3的单调性假设下,利用对称山路引理证明了无穷多个高能量解的存在性.此外,考虑了非线性项f次线性增长的情形并获得了解的存在性和多重性.
In this paper,we study the existence and multiplicity of solutions for the SchrodingerPoisson system{-△u+V(x)u+K(x)φu=f(x,u),x∈R^3,-△φ=K(x)u^2,x∈R^3,where V ∈ C(R^3,R) and K ∈ L^2 ∪ L^∞ with K 0.Without assuming the AmbrosettiRabinowitz type superquadratic condition and the monotonicity of the function t →(f(x,t))/t^3,we prove the existence of infinitely many high-energy solutions by using symmetric mountain pass theorem.We also consider the case where f is sublinear and establish the existence and multiplicity.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2015年第4期668-682,共15页
Acta Mathematica Scientia
基金
国家自然科学基金(11471267)
重庆师范大学基金项目(14XLB008)资助