Topological Methods in Nonlinear Analysis

Degree computations for positively homogeneous differential equations

Christian Fabry and Patrick Habets

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We study $2\pi$-periodic solutions of $$ u''+f(t,u)=0 $$ using positively homogeneous asymptotic approximations of this equation near zero and infinity. Our main results concern the degree of $I-P$, where $P$ is the Poincaré map associated to these approximations. We indicate classes of problems, some with degree 1 and others with degree different from 1. Considering results based on first order approximations, we work out examples of equations for which the degree is the negative of any integer.

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Topol. Methods Nonlinear Anal., Volume 23, Number 1 (2004), 73-88.

First available in Project Euclid: 31 May 2016

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Fabry, Christian; Habets, Patrick. Degree computations for positively homogeneous differential equations. Topol. Methods Nonlinear Anal. 23 (2004), no. 1, 73--88.

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