Infinitely many solutions for a class of $p(x)$-Kirchhoff type problems with critical exponents
Volume 124 / 2020
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.
