On radial solutions of inhomogeneous nonlinear scalar field equations

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the existence of radially symmetric solutions u∈H1(ω) of the following nonlinear scalar field equation -δu=g(|x|,u) in ω. Here ω=RN or {x∈RN||x|>R}, N≥2. We generalize the results of Li and Li (1993) [13] and Li (1990) [14] in which they studied the problem in RN and {|x|>R} with the Dirichlet boundary condition. Furthermore, we extend it to the Neumann boundary problem and we also consider the nonlinear Schrödinger equation that is the case g(r,s)=-V(r)s+g~(s).

Original languageEnglish
Pages (from-to)744-762
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume386
Issue number2
DOIs
Publication statusPublished - 2012 Feb 15
Externally publishedYes

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Radially Symmetric Solutions
Radial Solutions
Neumann Problem
Boundary Problem
Nonlinear equations
Dirichlet Boundary Conditions
Scalar Field
Nonlinear Equations
Boundary conditions
Generalise

Keywords

  • Monotonicity methods
  • Nonlinear scalar field equation
  • Radially symmetric solutions
  • Symmetric mountain pass argument

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On radial solutions of inhomogeneous nonlinear scalar field equations. / Ikoma, Norihisa.

In: Journal of Mathematical Analysis and Applications, Vol. 386, No. 2, 15.02.2012, p. 744-762.

Research output: Contribution to journalArticle

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