On computation of bounds of the bifurcation parameter for a non-local elliptic equation with increasing nonlinearity

Mohammed Al-Refai; Nikos I. Kavallaris

doi:10.1016/j.camwa.2013.05.020

On computation of bounds of the bifurcation parameter for a non-local elliptic equation with increasing nonlinearity

Mohammed Al-Refai, Nikos I. Kavallaris

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

A novel approach is developed to prove the existence of δ^∗, the supremum of the spectrum of a non-local elliptic problem associated with homogeneous Robin and Dirichlet boundary conditions. Analytical upper and lower bounds of δ^∗ are obtained in closed form. The bounds are presented for the slab, cylindrical and spherical geometries.

Original language	English
Pages (from-to)	512-524
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	66
Issue number	4
DOIs	https://doi.org/10.1016/j.camwa.2013.05.020
Publication status	Published - Sept 2013

Keywords

Bifurcation parameters
Moving plane method
Non-local elliptic problems

ASJC Scopus subject areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2013.05.020

Cite this

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title = "On computation of bounds of the bifurcation parameter for a non-local elliptic equation with increasing nonlinearity",

abstract = "A novel approach is developed to prove the existence of δ∗, the supremum of the spectrum of a non-local elliptic problem associated with homogeneous Robin and Dirichlet boundary conditions. Analytical upper and lower bounds of δ∗ are obtained in closed form. The bounds are presented for the slab, cylindrical and spherical geometries.",

keywords = "Bifurcation parameters, Moving plane method, Non-local elliptic problems",

author = "Mohammed Al-Refai and Kavallaris, {Nikos I.}",

note = "Publisher Copyright: {\textcopyright} 2013 Elsevier Ltd",

year = "2013",

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AU - Al-Refai, Mohammed

AU - Kavallaris, Nikos I.

PY - 2013/9

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N2 - A novel approach is developed to prove the existence of δ∗, the supremum of the spectrum of a non-local elliptic problem associated with homogeneous Robin and Dirichlet boundary conditions. Analytical upper and lower bounds of δ∗ are obtained in closed form. The bounds are presented for the slab, cylindrical and spherical geometries.

AB - A novel approach is developed to prove the existence of δ∗, the supremum of the spectrum of a non-local elliptic problem associated with homogeneous Robin and Dirichlet boundary conditions. Analytical upper and lower bounds of δ∗ are obtained in closed form. The bounds are presented for the slab, cylindrical and spherical geometries.

KW - Bifurcation parameters

KW - Moving plane method

KW - Non-local elliptic problems

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SP - 512

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 4

ER -

On computation of bounds of the bifurcation parameter for a non-local elliptic equation with increasing nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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