# Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree

@article{Feltrin2015MultiplicityOP,
title={Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree},
author={Guglielmo Feltrin and F. Zanolin},
journal={arXiv: Classical Analysis and ODEs},
year={2015}
}
• Published 2015
• Mathematics
• arXiv: Classical Analysis and ODEs
We study the periodic boundary value problem associated with the second order nonlinear differential equation $$u" + c u' + \left(a^{+}(t) - \mu \, a^{-}(t)\right) g(u) = 0,$$ where $g(u)$ has superlinear growth at zero and at infinity, $a(t)$ is a periodic sign-changing weight, $c\in\mathbb{R}$ and $\mu>0$ is a real parameter. We prove the existence of $2^{m}-1$ positive solutions when $a(t)$ has $m$ positive humps separated by $m$ negative ones (in a periodicity interval) and $\mu$ is… Expand

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