Normalized solutions for p-Laplacian equations with critical Sobolev exponent and mixed nonlinearities

In this paper, we consider the normalized solutions for the following [Formula: see text]-Laplacian critical equation: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is a Lagrange multiplier. Using the concentration compactness lemma, Schwarz rearrangement, Ekeland’s variational principle and minimax theorems, we obtain several existence results under [Formula: see text] and other suitable assumptions. We also analyze the asymptotic behavior of these solutions as [Formula: see text] and [Formula: see text] goes to its upper bound. Moreover, we show the nonexistence result for [Formula: see text] and get that the [Formula: see text]-Laplacian equation has infinitely many solutions by genus theory when [Formula: see text].