A fibering map approach to a semilinear elliptic boundary value problem

Kenneth J. Brown; Tsung Fang Wu

A fibering map approach to a semilinear elliptic boundary value problem

Kenneth J. Brown, Tsung Fang Wu

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

Abstract

We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u ^q + b(x)u^p for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. © 2007 Texas State University.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Electronic Journal of Differential Equations
Volume	2007
Publication status	Published - 10 May 2007

Keywords

Fibering map
Nehari manifold
Semilinear elliptic boundary value problem
Variational methods

Cite this

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title = "A fibering map approach to a semilinear elliptic boundary value problem",

abstract = "We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. {\textcopyright} 2007 Texas State University.",

keywords = "Fibering map, Nehari manifold, Semilinear elliptic boundary value problem, Variational methods",

author = "Brown, {Kenneth J.} and Wu, {Tsung Fang}",

year = "2007",

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language = "English",

volume = "2007",

pages = "1--9",

journal = "Electronic Journal of Differential Equations",

publisher = "Texas State University - San Marcos",

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T1 - A fibering map approach to a semilinear elliptic boundary value problem

AU - Brown, Kenneth J.

AU - Wu, Tsung Fang

PY - 2007/5/10

Y1 - 2007/5/10

N2 - We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. © 2007 Texas State University.

AB - We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. © 2007 Texas State University.

KW - Fibering map

KW - Nehari manifold

KW - Semilinear elliptic boundary value problem

KW - Variational methods

UR - http://www.scopus.com/inward/record.url?scp=34248386093&partnerID=8YFLogxK

M3 - Article

VL - 2007

SP - 1

EP - 9

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

A fibering map approach to a semilinear elliptic boundary value problem

Abstract

Keywords

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