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arXiv · 1503.05310

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

Alberto Boscaggin·Guglielmo Feltrin·Fabio Zanolin
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Abstract

We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation \begin{equation*} u'' + c u' + \lambda a(t) g(u) = 0, \end{equation*} where $g \colon \mathopen{[}0,+\infty\mathclose{[}\to \mathopen{[}0,+\infty\mathclose{[}$ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when $\int_{0}^{T} a(t) \!dt < 0$ and $\lambda > 0$ is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

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Alberto Boscaggin, Guglielmo Feltrin, Fabio Zanolin. 2015-03-18. Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case. https://arxiv.org/abs/1503.05310

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