Degree computations for positively homogeneous differential equations
KeywordsPeriodic solutions, Brouwer degree, Poincaré operator, positively homogeneous equation, Fučik spectrum
AbstractWe 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.
How to Cite
FABRY, Christian & HABETS, Patrick. Degree computations for positively homogeneous differential equations. Topological Methods in Nonlinear Analysis [online]. 1 March 2004, T. 23, nr 1, s. 73–88. [accessed 25.10.2021].
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