Normalized solutions of mass supercritical Schrodinger equations with potential

被引：83

作者：

Bartsch, Thomas ^{[1
]}

Molle, Riccardo ^{[2
]}

Rizzi, Matteo ^{[1
]}

Verzini, Gianmaria ^{[3
]}

机构：

[1] Justus Liebig Univ Giessen, Math Inst, Arndtstr 2, D-35392 Giessen, Germany

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Rome, Italy

[3] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci, Milan, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 46卷 / 09期

关键词：

Nonlinear Schrodinger equations; mln-max methods; normalized solution; POSITIVE SOLUTIONS;

D O I：

10.1080/03605302.2021.1893747

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the existence of normalized solutions of the nonlinear Schrodinger equation -Delta u + V(x)u + lambda u = vertical bar u vertical bar(p-2)u in R-N in the mass supercritical and Sobolev subcritical case 2 + 4/N < p < 2*. We prove the existence of a solution (u, lambda) is an element of H-1 (R-N) x R+ with prescribed L-2-norm parallel to u parallel to(2) = rho under various conditions on the potential V : R-N -> R, positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.

引用

页码：1729 / 1756

页数：28