Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

Ruyun Ma; Tianlan Chen; Haiyan Wang

doi:10.1016/j.jmaa.2016.05.038

Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

Ruyun Ma, Tianlan Chen, Haiyan Wang

Mathematical and Natural Sciences, School of (SMNS)

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let B_R be the ball of radius R in R^N with N≥2. We consider the nonconstant radial positive solutions of elliptic systems of the form −Δu+u=f(u,v)inB_R,−Δv+v=g(u,v)inB_R,∂_νu=∂_νv=0on∂B_R, 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 language	English (US)
Pages (from-to)	542-565
Number of pages	24
Journal	Journal of Mathematical Analysis and Applications
Volume	443
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.05.038
State	Published - Nov 1 2016

Keywords

Bifurcation
Neumann problem
Nonconstant radial solutions
Perron–Frobenius Theorem
Radial eigenvalue

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2016.05.038

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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",

year = "2016",

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doi = "10.1016/j.jmaa.2016.05.038",

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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 - 2016/11/1

Y1 - 2016/11/1

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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DO - 10.1016/j.jmaa.2016.05.038

M3 - Article

AN - SCOPUS:84969674566

SN - 0022-247X

VL - 443

SP - 542

EP - 565

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

Abstract

Keywords

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