Normalized solutions of mass supercritical Schrödinger equations with potential

By Thomas Bartsch, R. Molle, Matteo Rizzi, Gianmaria Verzini. Communications in Partial Differential Equations, 2020

154 citations recorded by the source corpus.

Abstract This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation in the mass supercritical and Sobolev subcritical case We prove the existence of a solution with prescribed L 2-norm under various conditions on the potential positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3b6ec9fa31e88d27d50e45327a4d2f7612b01d5b

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Normalized solutions to mass supercritical Schrödinger equations with negative potential (2021, methodology): “We recall the main strategy, referring to [7] for the details.”
Normalized solution to the Schrödinger equation with potential and general nonlinear term: Mass super-critical case (2021, background): “By constructing a suitable linking structure, the authors of [2] can obtain the existence of solutions with high Morse index.”
Normalized solutions for a Schrödinger equation with critical growth in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen (2021, unknown): “Associated with the L2-supercritical problems, we would like to cite [10], where the authors studied a problem involving vanishing potential.”