On a class of noncooperative fourth-order elliptic systems with nonlocal terms and critical growth
J. Korean Math. Soc. 2019 Vol. 56, No. 5, 1419-1439
https://doi.org/10.4134/JKMS.j180716
Published online September 1, 2019
Nguyen Thanh Chung
Quang Binh University
Abstract : In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li \cite{Li} combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.
Keywords : Kirchhoff type problems, noncooperative elliptic systems, fourth-order equations, critical exponents, concentration compactness principle
MSC numbers : 35J35, 35J50, 35B33, 35G30
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