Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (1): 54-60.

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The Existence of Solutions for Choquard Type Equation

Sun Xiaomei   

  1. College of Science, Huazhong Agricultural University, Wuhan 430070
  • Received:2017-01-13 Revised:2017-04-15 Online:2018-02-26 Published:2018-02-26
  • Supported by:
    Supported by the NSFC (11601173)

Abstract: In this paper, we consider the following Choquard type equation
pu+V(x)|u|p-2u=(|x|-(N-α) * F(u))f(u),
where -Δpu=div(|▽ u|p-2u) and x=(y,z)∈ RK×RN-K. Assume that the potential V(y,z) and the nonlinearity f satisfy suitable conditions, we prove the existence of solutions in the level of mountain pass for the above Choquard equation.

Key words: Choquard type equation, Mixted potential, Nontrivial solution

CLC Number: 

  • O175.25
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