Title:	Nodal solutions of weighted indefinite problems
Authors:	Fencl, Martin López-Gómez, Julián
Citation:	FENCL, M. LÓPEZ-GÓMEZ, J. Nodal solutions of weighted indefinite problems. JOURNAL OF EVOLUTION EQUATIONS, 2021, roč. 21, č. 3, s. 2815-2835. ISSN: 1424-3199
Issue Date:	2021
Publisher:	Birkhauser
Document type:	preprint preprint
URI:	2-s2.0-85092086230 http://hdl.handle.net/11025/46652
ISSN:	1424-3199
Keywords in different language:	Bifurcation;Concavity;Eigencurves;Finite-difference scheme;Global components;Nodal solutions;Path-following;Positive solutions;Pseudo-spectral methods;Superlinear indefinite problems;Weighted problems
Abstract in different language:	This paper analyzes the structure of the set of nodal solutions, i.e., solutions changing sign, of a class of one-dimensional superlinear indefinite boundary value problems with indefinite weight functions in front of the spectral parameter. Quite surprisingly, the associated high-order eigenvalues may not be concave as is the case for the lowest one. As a consequence, in many circumstances, the nodal solutions can bifurcate from three or even four bifurcation points from the trivial solution. This paper combines analytical and numerical tools. The analysis carried out is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously the numerical study confirms and illuminates the analysis.
Rights:	© Springer
Appears in Collections:	Preprinty / Preprints (KMA) OBD

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