Bifurcation from infinity for an asymptotically linear problem on the half-line

Francois Genoud

doi:10.1016/j.na.2011.04.019

Bifurcation from infinity for an asymptotically linear problem on the half-line

Francois Genoud

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

11 Citations (Scopus)

Abstract

This paper is concerned with asymptotic bifurcation for a semilinear equation on the half-line. For an asymptotically linear nonlinearity, the existence of a continuum of solutions 'bifurcating from infinity' is obtained by using a topological degree. Under additional monotonicity conditions, the continuum is shown to be a continuous curve. Applications to nonlinear planar waveguides are mentioned. © 2011 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	4533-4543
Number of pages	11
Journal	Nonlinear Analysis: Theory, Methods and Applications
Volume	74
Issue number	13
DOIs	https://doi.org/10.1016/j.na.2011.04.019
Publication status	Published - Sept 2011

Keywords

Asymptotic bifurcation
Nonlinear waveguides
Saturable nonlinearity
Topological degree
Unbounded domain

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10.1016/j.na.2011.04.019

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abstract = "This paper is concerned with asymptotic bifurcation for a semilinear equation on the half-line. For an asymptotically linear nonlinearity, the existence of a continuum of solutions 'bifurcating from infinity' is obtained by using a topological degree. Under additional monotonicity conditions, the continuum is shown to be a continuous curve. Applications to nonlinear planar waveguides are mentioned. {\textcopyright} 2011 Elsevier Ltd. All rights reserved.",

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AB - This paper is concerned with asymptotic bifurcation for a semilinear equation on the half-line. For an asymptotically linear nonlinearity, the existence of a continuum of solutions 'bifurcating from infinity' is obtained by using a topological degree. Under additional monotonicity conditions, the continuum is shown to be a continuous curve. Applications to nonlinear planar waveguides are mentioned. © 2011 Elsevier Ltd. All rights reserved.

KW - Asymptotic bifurcation

KW - Nonlinear waveguides

KW - Saturable nonlinearity

KW - Topological degree

KW - Unbounded domain

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DO - 10.1016/j.na.2011.04.019

M3 - Article

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SP - 4533

EP - 4543

JO - Nonlinear Analysis: Theory, Methods and Applications

JF - Nonlinear Analysis: Theory, Methods and Applications

IS - 13

ER -

Bifurcation from infinity for an asymptotically linear problem on the half-line

Abstract

Keywords

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