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

Fazekas, Borbála; Pacella, Filomena; Plum, Michael 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)


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.

Verlagsausgabe §
DOI: 10.5445/IR/1000137043
Veröffentlicht am 12.09.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 2191-9496, 2191-950X
KITopen-ID: 1000137043
Erschienen in Advances in Nonlinear Analysis
Verlag De Gruyter Open
Band 11
Heft 1
Seiten 268-284
Schlagwörter semilinear elliptic equations; bifurcation; sign changing solutions
Nachgewiesen in Web of Science
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