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Normalized solutions of mass supercritical Schrödinger equations with potential
Communications in Partial Differential Equations ( IF 2.1 ) Pub Date : 2021-03-10 , DOI: 10.1080/03605302.2021.1893747
Thomas Bartsch 1 , Riccardo Molle 2 , Matteo Rizzi 1 , Gianmaria Verzini 3
Affiliation  

Abstract

This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation Δu+V(x)u+λu=|u|p2uin RN in the mass supercritical and Sobolev subcritical case 2+4N<p<2*. We prove the existence of a solution (u,λ)H1(RN)×R+ with prescribed L2-norm u2=ρ under various conditions on the potential V:RNR, positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.



中文翻译:

具有势能的质量超临界薛定谔方程的归一化解

摘要

本文关注非线性薛定谔方程归一化解的存在性 Δ+(X)+λ=||2 电阻N 在质量超临界和 Sobolev 亚临界情况下 2+4N<<2*. 我们证明解的存在 (,λ)H1(电阻N)×电阻+具有规定的L 2 -范数2=ρ 在各种条件下对电势 :电阻N电阻,为正且在无穷远处消失,包括具有奇点的势。证明基于新的最小-最大参数。

更新日期:2021-03-10
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