On Neumann boundary value problems for some quasilinear elliptic equations
function $a(x)$ on the existence of positive solutions to the problem $$left{ eqalign{ -{ m div},(|abla u|^{p-2}abla u)&= lambda a(x)|u|^{p-2}u+b(x)|u|^{gamma-2}u, quad xinOmega, cr x{partial u overpartial n}&=0, quad xinpartialOmega,,} ight. $$ where $Omega$ is a smooth bounded domain in $...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Texas State University
1997-01-01
|
Series: | Electronic Journal of Differential Equations |
Subjects: | |
Online Access: | http://ejde.math.txstate.edu/Volumes/1997/05/abstr.html |
id |
doaj-824f62d6cbf246be90a3645c6570b7b3 |
---|---|
record_format |
Article |
spelling |
doaj-824f62d6cbf246be90a3645c6570b7b32020-11-24T22:30:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911997-01-01199705111On Neumann boundary value problems for some quasilinear elliptic equationsPaul A. BindingPavel DrabekYin Xi Huangfunction $a(x)$ on the existence of positive solutions to the problem $$left{ eqalign{ -{ m div},(|abla u|^{p-2}abla u)&= lambda a(x)|u|^{p-2}u+b(x)|u|^{gamma-2}u, quad xinOmega, cr x{partial u overpartial n}&=0, quad xinpartialOmega,,} ight. $$ where $Omega$ is a smooth bounded domain in $R^n$, $b$ changes sign, $1<p<N$, $1<gamma<Np/(N-p)$ and $gammae p$. We prove that (i) if $int_Omega a(x), dxe 0$ and $b$ satisfies another integral condition, then there exists some $lambda^*$ such that $lambda^* int_Omega a(x), dx<0$ and, for $lambda$ strictly between 0 and $lambda^*$, the problem has a positive solution. (ii) if $int_Omega a(x), dx=0$, then the problem has a positive solution for small $lambda$ provided that $int_Omega b(x),dx<0$. http://ejde.math.txstate.edu/Volumes/1997/05/abstr.htmlp-Laplacianpositive solutionsNeumann boundary value problems. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Paul A. Binding Pavel Drabek Yin Xi Huang |
spellingShingle |
Paul A. Binding Pavel Drabek Yin Xi Huang On Neumann boundary value problems for some quasilinear elliptic equations Electronic Journal of Differential Equations p-Laplacian positive solutions Neumann boundary value problems. |
author_facet |
Paul A. Binding Pavel Drabek Yin Xi Huang |
author_sort |
Paul A. Binding |
title |
On Neumann boundary value problems for some quasilinear elliptic equations |
title_short |
On Neumann boundary value problems for some quasilinear elliptic equations |
title_full |
On Neumann boundary value problems for some quasilinear elliptic equations |
title_fullStr |
On Neumann boundary value problems for some quasilinear elliptic equations |
title_full_unstemmed |
On Neumann boundary value problems for some quasilinear elliptic equations |
title_sort |
on neumann boundary value problems for some quasilinear elliptic equations |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
1997-01-01 |
description |
function $a(x)$ on the existence of positive solutions to the problem $$left{ eqalign{ -{ m div},(|abla u|^{p-2}abla u)&= lambda a(x)|u|^{p-2}u+b(x)|u|^{gamma-2}u, quad xinOmega, cr x{partial u overpartial n}&=0, quad xinpartialOmega,,} ight. $$ where $Omega$ is a smooth bounded domain in $R^n$, $b$ changes sign, $1<p<N$, $1<gamma<Np/(N-p)$ and $gammae p$. We prove that (i) if $int_Omega a(x), dxe 0$ and $b$ satisfies another integral condition, then there exists some $lambda^*$ such that $lambda^* int_Omega a(x), dx<0$ and, for $lambda$ strictly between 0 and $lambda^*$, the problem has a positive solution. (ii) if $int_Omega a(x), dx=0$, then the problem has a positive solution for small $lambda$ provided that $int_Omega b(x),dx<0$. |
topic |
p-Laplacian positive solutions Neumann boundary value problems. |
url |
http://ejde.math.txstate.edu/Volumes/1997/05/abstr.html |
work_keys_str_mv |
AT paulabinding onneumannboundaryvalueproblemsforsomequasilinearellipticequations AT paveldrabek onneumannboundaryvalueproblemsforsomequasilinearellipticequations AT yinxihuang onneumannboundaryvalueproblemsforsomequasilinearellipticequations |
_version_ |
1725741741763461120 |