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

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 approa...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2016-06, Vol.146 (3), p.449-474
Main Authors: Boscaggin, Alberto, Feltrin, Guglielmo, Zanolin, Fabio
Format: Article
Language:English
Subjects:
Boundary value problems
Computation
Differential equations
Infinity
Mathematical analysis
Mathematical models
Nonlinear equations
Nonlinearity
Topology
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Summary: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210515000621