Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1590-1598.

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Nontrivial Solution for Schrödinger-Poisson type Systems with Double Critical Terms

Xiaojing Feng()   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006
  • Received:2019-11-06 Online:2020-12-26 Published:2020-12-29
  • Supported by:
    the NSFC(11571209);the NSFC(11671239);NSF of Shanxi Province(201801D211001);NSF of Shanxi Province(201801D121002);NSF of Shanxi Province(201801D221012);the Shanxi Scholarship Council(020-005)


The existence of a nontrivial solution to the Schrödinger-Poisson type system with both nonlinear critical growth and nonlocal critical growth is obtained by applying the concentration-compactness principle and mountain pass theorem. The double critical growth in the system presents an obstacle when showing the convergence of the bounded (PS) sequences. At the same time, it is difficult to estimate the critical level of the mountain pass. The key ingredient of the paper is to show that the critical level of the mountain pass is below the non-compactness level of the associated energy functional.

Key words: Schrödinger-Poisson type system, Critical exponent, Variational method

CLC Number: 

  • O175.2