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

2023/06/11 by Deng, Shengbing, Wu, Qiaoran
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.06709

Abstract

In this paper, we consider the existence and multiplicity of normalized solutions for the following p-Laplacian critical equation \-Δ_pu=λ| u|^p-2u+μ| u|^q-2u+| u|^{p^*-1}u · amp;in ℝ^N, ∫_ℝ^N| u|^pdx=a^p,. where 10, μ∈ℝ and λ∈ℝ is a Lagrange multiplier. Using concentration compactness lemma, Schwarz rearrangement, Ekeland variational principle and mini-max theorems, we obtain several existence results under μ>0 and other assumptions. We also analyze the asymptotic behavior of there solutions as μ→ 0 and μ goes to its upper bound. Moreover, we show the nonexistence result for μ<0 and get that the p-Laplacian equation has infinitely solutions by genus theory when p

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