On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in ℝN-Reference-Cited by-同舟云学术

On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in ℝN

Published:2007-08-01 Issue:3 Volume:7 Page:439-458
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Bellazzini J.¹,Ghimenti V. Benci M.¹,Micheletti A.M.¹

Affiliation:

1. Dipartimento di Matematica Applicata, Universitá di Pisa, Via Buonarroti 1/C 56127 PISA -Italy

Abstract

Abstract We study an eigenvalue problem for functions in ℝN and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability of the standing waves of the nonlinear Schrödinger equation.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2007-0306/pdf

Reference10 articles.

1. Bifurcation from the essential spectrum for some non compact nonlinear - ities;Stuart;Proc London Math Soc,1988

2. The concentration - compactness principle in the Calculus of Variations The locally compact case part Henri Poincare The concentration - compactness principle in the Calculus of Variations The locally compact case part Henri Poincare;Lions;Inst Inst,1984

3. Decay and scattering of solutions of a nonlinear Schro dinger equation;Lin;Funct Anal,1978

4. Comments on nonlinear wave equations as models for elementary parti - cles;Derrick;Commun Math Phys,1964

5. Nonlinear scalar field equations Existence of a ground state Arch Rational;Berestycki;Mech Anal,1982

Cited by 17 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Stability and instability of standing-wave solutions to one-dimensional quadratic-cubic Klein–Gordon equations;Journal of Fixed Point Theory and Applications;2023-04-04

2. Normalized solutions to the Schrödinger systems with double critical growth and weakly attractive potentials;Electronic Journal of Qualitative Theory of Differential Equations;2023

3. Orbital stability and concentration of standing-wave solutions to a nonlinear Schrödinger system with mass critical exponents;Nonlinear Differential Equations and Applications NoDEA;2022-10-28

4. Existence and Stability of Standing Waves with Prescribed <i>L</i><sup>2</sup>-Norm for a Class of Schr&#246;dinger-Bopp-Podolsky System;Journal of Applied Mathematics and Physics;2022

5. Multiple normalized standing-wave solutions to the scalar non-linear Klein-Gordon equation with two competing powers;Journal of Differential Equations;2020-11