带有超线性项或次线性项的Schrodinger-Poisson系统解的存在性和多重性

Existence and Multiplicity Results for Schrdinger-Poisson System with Superlinear or Sublinear Terms

该文研究如下Schrdinger-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.