Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 730-748.

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Ground State Solutions for Quasilinear Schrödinger Equation of Choquard Type

Yanan Wang(),Kaimin Teng*()   

  1. School of Mathematical, Taiyuan University of Technology, Shanxi Jinzhong 030600
  • Received:2021-04-14 Online:2022-06-26 Published:2022-05-09
  • Contact: Kaimin Teng;
  • Supported by:
    the NSFC(11501403);the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(2018);the NSF of Shanxi Province(201901D111085)


In this paper, we consider the following quasilinear Schrödinger equations of Choquard type where $N\geq3$, 0 < $\alpha$ < $N$, $<p<\frac{N+\alpha}{N-2}$, $I_{\alpha}$ is the Riesz potential, $V(x)$ is a positive continuous potential and $k$ is a non-negative parameter. The existence of ground state solutions is established via Pohožaev manifold approach.

Key words: Choquard type problems, Pohožaev manifold, Ground state solutions

CLC Number: 

  • O175.25