Degree computations for positively homogeneous differential equations
Keywords
Periodic solutions, Brouwer degree, Poincaré operator, positively homogeneous equation, Fučik spectrumAbstract
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.Downloads
Published
2004-03-01
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1.
FABRY, Christian and HABETS, Patrick. Degree computations for positively homogeneous differential equations. Topological Methods in Nonlinear Analysis. Online. 1 March 2004. Vol. 23, no. 1, pp. 73 - 88. [Accessed 23 April 2024].
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