Journal of the
Korean Mathematical Society JKMS

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

Supported by: This research is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) (Grant N.101.02.2017.04).