Approximate nonradial solutions for the Lane-Emden problem in the ball

In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ2, as the exponent of the nonlinearity varies. We consider solutions with two or three nodal regions. In the first case our numerical result...

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Autores principales:	Fazekas Borbála, Pacella Filomena, Plum Michael
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	semilinear elliptic equations bifurcation sign changing solutions 35j15 35j60 35b06 35b32 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/98dbbb81b61b46b0841fbb04ff98585d
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spelling	oai:doaj.org-article:98dbbb81b61b46b0841fbb04ff98585d2021-12-05T14:10:40ZApproximate nonradial solutions for the Lane-Emden problem in the ball2191-94962191-950X10.1515/anona-2020-0191https://doaj.org/article/98dbbb81b61b46b0841fbb04ff98585d2021-08-01T00:00:00Zhttps://doi.org/10.1515/anona-2020-0191https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XIn this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ2, as the exponent of the nonlinearity varies. We consider solutions with two or three nodal regions. In the first case our numerical results complement the analytical ones recently obtained in [11]. In the case of solutions with three nodal regions, for which no analytical results are available, our analysis gives numerical evidence of the existence of bifurcation branches. We also compute additional approximations indicating presence of an unexpected branch of solutions with six nodal regions. In all cases the numerical results allow to formulate interesting conjectures.Fazekas BorbálaPacella FilomenaPlum MichaelDe Gruyterarticlesemilinear elliptic equationsbifurcationsign changing solutions35j1535j6035b0635b32AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 268-284 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	semilinear elliptic equations bifurcation sign changing solutions 35j15 35j60 35b06 35b32 Analysis QA299.6-433
spellingShingle	semilinear elliptic equations bifurcation sign changing solutions 35j15 35j60 35b06 35b32 Analysis QA299.6-433 Fazekas Borbála Pacella Filomena Plum Michael Approximate nonradial solutions for the Lane-Emden problem in the ball
description	In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ2, as the exponent of the nonlinearity varies. We consider solutions with two or three nodal regions. In the first case our numerical results complement the analytical ones recently obtained in [11]. In the case of solutions with three nodal regions, for which no analytical results are available, our analysis gives numerical evidence of the existence of bifurcation branches. We also compute additional approximations indicating presence of an unexpected branch of solutions with six nodal regions. In all cases the numerical results allow to formulate interesting conjectures.
format	article
author	Fazekas Borbála Pacella Filomena Plum Michael
author_facet	Fazekas Borbála Pacella Filomena Plum Michael
author_sort	Fazekas Borbála
title	Approximate nonradial solutions for the Lane-Emden problem in the ball
title_short	Approximate nonradial solutions for the Lane-Emden problem in the ball
title_full	Approximate nonradial solutions for the Lane-Emden problem in the ball
title_fullStr	Approximate nonradial solutions for the Lane-Emden problem in the ball
title_full_unstemmed	Approximate nonradial solutions for the Lane-Emden problem in the ball
title_sort	approximate nonradial solutions for the lane-emden problem in the ball
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/98dbbb81b61b46b0841fbb04ff98585d
work_keys_str_mv	AT fazekasborbala approximatenonradialsolutionsforthelaneemdenproblemintheball AT pacellafilomena approximatenonradialsolutionsforthelaneemdenproblemintheball AT plummichael approximatenonradialsolutionsforthelaneemdenproblemintheball
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Approximate nonradial solutions for the Lane-Emden problem in the ball

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