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

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Existence and Multiplicity Results for Schrödinger-Poisson System with Superlinear or Sublinear Terms

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Abstract:

In this paper, we study the existence and multiplicity of solutions for the Schrödinger-Poisson system
where V∈ C(R³, R) and K∈ L²∪ L^∞ with K≥ 0. Without assuming the Ambrosetti-Rabinowitz type superquadratic condition and the monotonicity of the function t→(f(x,t))/(t³), 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.

Key words: Schrö, dinger-Poisson system, Superlinear, Sublinear, Infinitely many solutions, Variational methods

CLC Number:

O176.3

Ye Yiwei, Tang Chunlei. Existence and Multiplicity Results for Schrödinger-Poisson System with Superlinear or Sublinear Terms[J].Acta mathematica scientia,Series A, 2015, 35(4): 668-682.

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