一类具有临界指数和不定位势的Kirchhoff型问题解的存在性

doi:10.16088/j.issn.1001-6600.2023030402

Abstract

Abstract: In this paper, the existence of solutions for a class of Kirchhoff type problems with critical exponent and indefinite potential is studied. Firstly, the energy functional is proved to satisfy the mountain pass geometry. Secondly, the compactness condition of function is obtained by proving that the energy functional satisfies the local (PS)_c condition. Finally, the existence of two nontrivial solutions is obtained via Ekeland’s variational principle and the mountain pass lemma.

Key words: Kirchhoff type equations, critical exponent, indefinite potential, variational method

CLC Number: O177.9

GUO Jie, SUO Hongmin, ZHU Yiying, GUO Jiachao. Existence of Solutions for a Class of Kirchhoff Type Problems with Critical Exponent and Indefinite Potential[J].Journal of Guangxi Normal University(Natural Science Edition), 2023, 41(6): 105-112.

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Existence of Solutions for a Class of Kirchhoff Type Problems with Critical Exponent and Indefinite Potential

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