Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 23, Number 1 (2004), 73-88.
Degree computations for positively homogeneous differential equations
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.
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. https://projecteuclid.org/euclid.tmna/1464731379