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Infinitely many solutions for a class of $p(x)$-Kirchhoff type problems with critical exponents

Volume 124 / 2020

Nguyen Thanh Chung Annales Polonici Mathematici 124 (2020), 129-149 MSC: Primary 35J60; Secondary 35J20, 35J66, 35J92. DOI: 10.4064/ap180827-11-6 Published online: 24 January 2020

Abstract

We consider a class of $p(x)$-Kirchhoff type problems with critical exponents in bounded domains. Under some conditions on the nonlinearities, we establish the existence of infinitely many solutions for the problem in a Sobolev space with variable exponent by using the genus theory introduced by Krasnosel’skiĭ and a variant of the mountain pass theorem in critical point theory. Our results complement and improve some previous ones on nonlocal problems with critical growth.

Authors

  • Nguyen Thanh ChungDepartment of Mathematics
    Quang Binh University
    312 Ly Thuong Kiet
    Dong Hoi, Quang Binh, Viet Nam
    e-mail

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