Three nodal solutions of singularly perturbed elliptic equations on domains without topology

By Thomas Bartsch, Tobias Weth. 2005

214 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d00c0d7cab9f985cbcbae47413d751e6573459b0

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$R3 (2015, background): “Motivated by [6], in order to obtain sign-changing solution for the problem (1.”
Desingularization of Vortices for the Euler Equation (2009, methodology): “It is a standard procedure [6–8,16] to prove that Proposition 5.”
Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains (2013, background): “ estimates, see Section 2 for details. Before to conclude this introduction, we would like to cite the papers of Alves [1], Alves & Soares [2, 3], Bartsch, Weth and Willem [6], Bartsch & Weth [7], Bartsch, Liu & Weth [8], Castro, Cossio & Neuberger [12], Zou [30] and their references”
Partial symmetry of least energy nodal solutions to some variational problems (2005, background): “Note that assumptions (A1) - (A3) do not guarantee that the infimum B is attained in M. Nevertheless, the existence of a minimizer u E M of �9 has been established under various additional conditions on f/and f; see [9, 3, 4, 5 ].”
Normalized solutions of mass supercritical Schrödinger equations with potential (2020, background): “th RN, however the proof is exactly the same. We stress that exactly here we need λ > 0, as in [9]. Now we recall the notion of barycentre of a function u ∈ H1(RN)\{0} which has been introduced in [7] and in [13]. Setting (3.15) ν(u)(x) = 1 |B1(0)| Z B1(x) |u(y)|dy, we observe that ν(u) is bounde”
The existence of least energy nodal solutions for some class of Kirchhoff equations and Choquard equations (2015, methodology): “5) in bounded domains are proved to exist by Noussair and Wei in [29] via the Ekeland variational principle and the implicit function theorem, and by Bartsch and Weth in [6] based on the variational method together with the Brouwer degree theory.”
Sign-changing solutions for the nonlinear Schrödinger–Poisson system in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen (2014, methodology): “3, which cannot be done in a similar way as [7], we do it successfully by using the fact that zeros of analytic functions are isolated.”