On solutions of two-point boundary value problems inside isolating segments
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Boundary value problem, isolating segment, Lefschetz number, fixed point indexAbstrakt
We consider a two-point boundary value problem $$ \dot x=f(t,x), \quad x(a)=g(x(b)). $$ We assume that in the extended space of the equation there exist an isolating segment, a set such that $f$ properly behaves on its boundary. We give a formula for the fixed point index of the composition of $g$ with the translation operator in a neighbourhood of the set of the initial points of solutions contained in the isolating segment. We apply that formula to results on existence of solutions of some planar boundary value problem associated to equations of the form $\dot z=\overline z^q+\ldots$ and $\dot z=e^{it}\overline z^q+\ldots$.Pobrania
Opublikowane
1999-03-01
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1.
SRZEDNICKI, Roman. On solutions of two-point boundary value problems inside isolating segments. Topological Methods in Nonlinear Analysis [online]. 1 marzec 1999, T. 13, nr 1, s. 73–89. [udostępniono 22.7.2024].
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