New approaches for Schrödinger equations with prescribed mass: The Sobolev subcritical case and The Sobolev critical case with mixed dispersion

2022/10/26 by Chen, Sitong, Tang, Xianhua · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.14503

Abstract

In this paper, we prove the existence of normalized solutions for the following Schrödinger equation \ -Δu-λu=f(u), · amp; x∈ \R^N, ∫_\R^Nu²dx=c . with N≥3, c>0, λ∈ \R and f∈ C(\R,\R) in the Sobolev subcritical case with weaker L²-supercritical conditions and in the Sobolev critical case when f(u)=μ|u|^q-2u+|u|^{2^*-2}u with μ>0 and 2

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