Multiplicity results for nonlinear elliptic equations
Let $Omega$ be a bounded domain in $mathbb{R}^{N}$, $Ngeq 3$, and $p=frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $fin H^1_0(Omega)^ast$, satisfying suitable conditions, the nonlinear elliptic problem $$displaylines{ -Delta u =|u |^{ p-2 }u +f quad hbox{in } Omega cr u=0 quad hbox{...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Texas State University
2006-09-01
|
Series: | Electronic Journal of Differential Equations |
Subjects: | |
Online Access: | http://ejde.math.txstate.edu/conf-proc/14/b2/abstr.html |
id |
doaj-d13746dfb1964def87d82cfd943873c9 |
---|---|
record_format |
Article |
spelling |
doaj-d13746dfb1964def87d82cfd943873c92020-11-25T00:34:30ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-09-01Conference14149153Multiplicity results for nonlinear elliptic equationsSamira BenmouloudMostafa KhiddiSimohammed SbaiLet $Omega$ be a bounded domain in $mathbb{R}^{N}$, $Ngeq 3$, and $p=frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $fin H^1_0(Omega)^ast$, satisfying suitable conditions, the nonlinear elliptic problem $$displaylines{ -Delta u =|u |^{ p-2 }u +f quad hbox{in } Omega cr u=0 quad hbox{on } partialOmega }$$ has at least three solutions in $H_{0}^{1}(Omega)$. http://ejde.math.txstate.edu/conf-proc/14/b2/abstr.htmlSemilinear elliptic equationscritical Sobolev exponent. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Samira Benmouloud Mostafa Khiddi Simohammed Sbai |
spellingShingle |
Samira Benmouloud Mostafa Khiddi Simohammed Sbai Multiplicity results for nonlinear elliptic equations Electronic Journal of Differential Equations Semilinear elliptic equations critical Sobolev exponent. |
author_facet |
Samira Benmouloud Mostafa Khiddi Simohammed Sbai |
author_sort |
Samira Benmouloud |
title |
Multiplicity results for nonlinear elliptic equations |
title_short |
Multiplicity results for nonlinear elliptic equations |
title_full |
Multiplicity results for nonlinear elliptic equations |
title_fullStr |
Multiplicity results for nonlinear elliptic equations |
title_full_unstemmed |
Multiplicity results for nonlinear elliptic equations |
title_sort |
multiplicity results for nonlinear elliptic equations |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2006-09-01 |
description |
Let $Omega$ be a bounded domain in $mathbb{R}^{N}$, $Ngeq 3$, and $p=frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $fin H^1_0(Omega)^ast$, satisfying suitable conditions, the nonlinear elliptic problem $$displaylines{ -Delta u =|u |^{ p-2 }u +f quad hbox{in } Omega cr u=0 quad hbox{on } partialOmega }$$ has at least three solutions in $H_{0}^{1}(Omega)$. |
topic |
Semilinear elliptic equations critical Sobolev exponent. |
url |
http://ejde.math.txstate.edu/conf-proc/14/b2/abstr.html |
work_keys_str_mv |
AT samirabenmouloud multiplicityresultsfornonlinearellipticequations AT mostafakhiddi multiplicityresultsfornonlinearellipticequations AT simohammedsbai multiplicityresultsfornonlinearellipticequations |
_version_ |
1725313068963987456 |