A switch in nodal structure in coupled systems of nonlinear Sturm-Liouville boundary value problems

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Abstract

It is well known that the bifurcating nontrivial solutions to nonlinear Sturm-Liouville boundary value problems may be globally distinguished via the nodal structure of solutions. We demonstrate in this article that such is not necessarily the case for appropriate coupled multiparameter systems of such problems. Specifically, we give a calculable condition for the existence of a continuum of nontrivial solutions to such a system where the nodal structure of solution components is not preserved.

Original languageEnglish (US)
Pages (from-to)1009-1028
Number of pages20
JournalRocky Mountain Journal of Mathematics
Volume21
Issue number3
DOIs
StatePublished - Jun 1991

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Sturm-Liouville
Nontrivial Solution
Coupled System
Switch
Boundary Value Problem
Continuum
Demonstrate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "A switch in nodal structure in coupled systems of nonlinear Sturm-Liouville boundary value problems",
abstract = "It is well known that the bifurcating nontrivial solutions to nonlinear Sturm-Liouville boundary value problems may be globally distinguished via the nodal structure of solutions. We demonstrate in this article that such is not necessarily the case for appropriate coupled multiparameter systems of such problems. Specifically, we give a calculable condition for the existence of a continuum of nontrivial solutions to such a system where the nodal structure of solution components is not preserved.",
author = "Robert Cantrell",
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