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.
Citation
Christian Fabry. Patrick Habets. "Degree computations for positively homogeneous differential equations." Topol. Methods Nonlinear Anal. 23 (1) 73 - 88, 2004.
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