Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution

Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution

We consider the equation $\Delta u+f(u)=0$ on a surface of revolution with Dirichlet boundary conditions. We obtain conditions on $f$, the geometry of the surface and the maximum value of a positive solution in order to ensure its stability or instability. Applications are given for our main results...

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Bibliographic Details
Main Author: Maicon Sônego
Format: Article
Language:English
Published: University of Szeged 2016-10-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Subjects:
surface of revolution
stability or instability of solutions
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5060
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spelling doaj-ce70cc3954ad430b8c09b9a5e85fa7552021-07-14T07:21:29ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752016-10-0120169511210.14232/ejqtde.2016.1.955060Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolutionMaicon Sônego0Universidade Federal de Itajubá, Itajubá, M.G., BrasilWe consider the equation $\Delta u+f(u)=0$ on a surface of revolution with Dirichlet boundary conditions. We obtain conditions on $f$, the geometry of the surface and the maximum value of a positive solution in order to ensure its stability or instability. Applications are given for our main results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5060surface of revolutionstability or instability of solutions
collection DOAJ
language English
format Article
sources DOAJ
author Maicon Sônego
spellingShingle Maicon Sônego
Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution
Electronic Journal of Qualitative Theory of Differential Equations
surface of revolution
stability or instability of solutions
author_facet Maicon Sônego
author_sort Maicon Sônego
title Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution
title_short Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution
title_full Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution
title_fullStr Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution
title_full_unstemmed Stability and instability of solutions of semilinear problems with Dirichlet boundary condition on surfaces of revolution
title_sort stability and instability of solutions of semilinear problems with dirichlet boundary condition on surfaces of revolution
publisher University of Szeged
series Electronic Journal of Qualitative Theory of Differential Equations
issn 1417-3875
1417-3875
publishDate 2016-10-01
description We consider the equation $\Delta u+f(u)=0$ on a surface of revolution with Dirichlet boundary conditions. We obtain conditions on $f$, the geometry of the surface and the maximum value of a positive solution in order to ensure its stability or instability. Applications are given for our main results.
topic surface of revolution
stability or instability of solutions
url http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5060
work_keys_str_mv AT maiconsonego stabilityandinstabilityofsolutionsofsemilinearproblemswithdirichletboundaryconditiononsurfacesofrevolution
_version_ 1721303520725958656

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