Multiple Solutions for a Non-cooperative Elliptic System of Kirchhoff Type Involving \(p\)-Biharmonic Operator and Critical Growth

  • Nguyen Thanh ChungEmail author


In this paper, we consider a class of non-cooperative elliptic systems of Kirchhoff type involving \(p\)-biharmonic operator and critical growth. With the help of the Limit index theory due to Li (Nonlinear Anal. TMA 30(7):4619–4627, 1997) and the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity.


Non-cooperative elliptic system Kirchhoff type problem \(p\)-Biharmonic operator Critical exponents Concentration compactness principle Limit index theory 

Mathematics Subject Classification

34B15 34B18 35J35 35G30 



The author would like to thank the referees for their suggestions and helpful comments which improved the presentation of the original manuscript. This research is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) (Grant N.101.02.2017.04).


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsQuang Binh UniversityDong HoiVietnam

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