JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 81-87.doi: 10.6040/j.issn.1671-9352.0.2018.620

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Existence of infinitely many high energy solutions of a class of fourth-order elliptic equations with nonlocal terms

ZHANG Nian, JIA Gao*   

  1. School of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Published:2019-06-05

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Abstract: We study a class of fourth-order elliptic equations with nonlocal term,{Δ2u-(a+b∫RN|∇u|2dx)Δu+V(x)u-1/2Δ(u2)u=f(x,u), x∈RN,u(x)∈H 2(RN),Where N≤5, constants a>0, b≥0, Δ2=Δ(Δ)is the biharmonic operater, the nonlinearity f(x,u) doesnt satisfy AR condition and the potential function V(x) is also allowed to be sign-changing. We establish the existence of a sequence of high energy weak solutions for this class of elliptic equations via variational methods.

Key words: Kirchhoff type equation, sign-changing potential, variational methods, Fountain theorem, infinitely many solutions

CLC Number: 

  • O175
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