Existence of ground state solution for critical N -Laplacian Kirchhoff-type problem with convolution nonlinearity
Lizhen Lai, Dongdong Qin, Die Hu, Jing Zhang · Bulletin of Mathematical Sciences · 2025
In this paper, we investigate the following N-Laplacian Kirchhoff–Choquard-type equation involving the critical exponential growth nonlinearity of Trudinger–Moser-type: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. We develop some delicate analyses to deal with the challenges caused by the quasilinear characteristic and the convolution term. By employing variational methods, we establish the existence of the ground state solution for above equation and succeed in finding a fine threshold to control the minimax level. In particular, for the autonomous case where [Formula: see text], the ground state solution is established by using the concentration compactness argument and some detailed estimates.