Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

Ruyun Ma, Tianlan Chen, Haiyan Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let BR be the ball of radius R in RN with N≥2. We consider the nonconstant radial positive solutions of elliptic systems of the form. -δu+u=f(u,v)inBR,-δv+v=g(u,v)inBR,∂νu=∂νv=0on∂BR, where f and g are nondecreasing in each component. With few assumptions on the nonlinearities, we apply bifurcation theory to show the existence of at least one nonnegative, nonconstant and nondecreasing solution.

Original languageEnglish (US)
JournalJournal of Mathematical Analysis and Applications
DOIs
StateAccepted/In press - Feb 3 2016

Fingerprint

Positive Radial Solutions
Bifurcation Theory
Elliptic Systems
Neumann Boundary Conditions
Ball
Non-negative
Radius
Boundary conditions
Nonlinearity
Form

Keywords

  • Bifurcation
  • Neumann problem
  • Nonconstant radial solutions
  • Perron-Frobenius Theorem
  • Radial eigenvalue

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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title = "Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions",
abstract = "Let BR be the ball of radius R in RN with N≥2. We consider the nonconstant radial positive solutions of elliptic systems of the form. -δu+u=f(u,v)inBR,-δv+v=g(u,v)inBR,∂νu=∂νv=0on∂BR, where f and g are nondecreasing in each component. With few assumptions on the nonlinearities, we apply bifurcation theory to show the existence of at least one nonnegative, nonconstant and nondecreasing solution.",
keywords = "Bifurcation, Neumann problem, Nonconstant radial solutions, Perron-Frobenius Theorem, Radial eigenvalue",
author = "Ruyun Ma and Tianlan Chen and Haiyan Wang",
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doi = "10.1016/j.jmaa.2016.05.038",
language = "English (US)",
journal = "Journal of Mathematical Analysis and Applications",
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T1 - Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

AU - Ma, Ruyun

AU - Chen, Tianlan

AU - Wang, Haiyan

PY - 2016/2/3

Y1 - 2016/2/3

N2 - Let BR be the ball of radius R in RN with N≥2. We consider the nonconstant radial positive solutions of elliptic systems of the form. -δu+u=f(u,v)inBR,-δv+v=g(u,v)inBR,∂νu=∂νv=0on∂BR, where f and g are nondecreasing in each component. With few assumptions on the nonlinearities, we apply bifurcation theory to show the existence of at least one nonnegative, nonconstant and nondecreasing solution.

AB - Let BR be the ball of radius R in RN with N≥2. We consider the nonconstant radial positive solutions of elliptic systems of the form. -δu+u=f(u,v)inBR,-δv+v=g(u,v)inBR,∂νu=∂νv=0on∂BR, where f and g are nondecreasing in each component. With few assumptions on the nonlinearities, we apply bifurcation theory to show the existence of at least one nonnegative, nonconstant and nondecreasing solution.

KW - Bifurcation

KW - Neumann problem

KW - Nonconstant radial solutions

KW - Perron-Frobenius Theorem

KW - Radial eigenvalue

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