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Positive solutions to Sturm–Liouville problems with non-local boundary conditions

Published online by Cambridge University Press:  30 January 2014

T. Jankowski
T. Jankowski*
Affiliation:
Differential Equations and Applied Mathematics, Gdańsk University of Technology, 80233 Gdańsk, Poland (tjank@mif.pg.gda.pl)
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Abstract

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In this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ϛ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 1 , February 2014 , pp. 119 - 138
Copyright
Copyright © Royal Society of Edinburgh 2014