Normalized solutions to $p$-Laplacian equation: Sobolev critical case

Abstract

This paper is devoted to the study of normalized solutions to $p$-Laplacian equation involving Sobolev critical exponent. Under the focussing condition, we obtain existence of ground states in mass subcritical case, mass critical case and mass supercritical case, respectively. Furthermore, we show some asymptotic behaviors of ground states. Meanwhile, under the defocussing condition, we prove some non-existence results.