RESEARCH ARTICLE

Multiplicity of nontrivial solutions for Kirchhoff type equations with zero mass and a critical term

  • Chongqing WEI ,
  • Anran LI
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  • School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Published date: 15 Oct 2022

Copyright

2022 Higher Education Press 2022

Abstract

In this paper, a class of Kirchhoff type equations in RN(N3) with zero mass and a critical term is studied. Under some appropriate conditions, the existence of multiple solutions is obtained by using variational methods and a variant of Symmetric Mountain Pass theorem. The Second Concentration Compactness lemma is used to overcome the lack of compactness in critical problem. Compared to the usual Kirchhoff-type problems, we only require the nonlinearity to satisfy the classical superquadratic condition (Ambrosetti-Rabinowitz condition).

Cite this article

Chongqing WEI , Anran LI . Multiplicity of nontrivial solutions for Kirchhoff type equations with zero mass and a critical term[J]. Frontiers of Mathematics in China, 2022 , 17(5) : 813 -828 . DOI: 10.1007/s11464-022-1028-8

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11701346, 11671239, 11801338), the Natural Science Foundation of Shanxi Province (Grant No. 201801D211001), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2019L0024), and the Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2020-005).
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