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Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super–sublinear case

Part of: Qualitative theory Boundary value problems Nonlinear operators and their properties

Published online by Cambridge University Press:  16 May 2016

Alberto Boscaggin ,
Guglielmo Feltrin  and
Fabio Zanolin
Alberto Boscaggin
Affiliation:
Dipartimento di Matematica ‘Giuseppe Peano’, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy ([email protected])
Guglielmo Feltrin
Affiliation:
SISSA – International School for Advanced Studies, via Carlo Alberto 10, via Bonomea 265, 34136 Trieste, Italy ([email protected])
Fabio Zanolin
Affiliation:
Dipartimento di Matematica, Informatica e Fisica, Università di Udine, via delle Scienze 206, 33100 Udine, Italy([email protected])
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Extract

We study the periodic and Neumann boundary-value problems associated with the second-order nonlinear differential equation

where is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when

and λ > 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

Keywords

boundary-value problemspositive solutionsindefinite weightmultiplicity resultscoincidence degree

MSC classification

Secondary: 34B18: Positive solutions of nonlinear boundary value problems 34C25: Periodic solutions 34B15: Nonlinear boundary value problems 47H11: Degree theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 3 , June 2016 , pp. 449 - 474
Copyright
Copyright © Royal Society of Edinburgh 2016 

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