Topological Methods in Nonlinear Analysis

Degree computations for positively homogeneous differential equations

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 31 May 2016

https://projecteuclid.org/euclid.tmna/1464731379

Mathematical Reviews number (MathSciNet)
MR2055327

Zentralblatt MATH identifier
1059.34002

Citation

Fabry, Christian; Habets, Patrick. Degree computations for positively homogeneous differential equations. Topol. Methods Nonlinear Anal. 23 (2004), no. 1, 73--88. https://projecteuclid.org/euclid.tmna/1464731379

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