On solutions of two-point boundary value problems inside isolating segments
Keywords
Boundary value problem, isolating segment, Lefschetz number, fixed point indexAbstract
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 $\dot z=e^{it}\overline z^q+\ldots$.Downloads
Published
1999-03-01
How to Cite
1.
SRZEDNICKI, Roman. On solutions of two-point boundary value problems inside isolating segments. Topological Methods in Nonlinear Analysis. Online. 1 March 1999. Vol. 13, no. 1, pp. 73 - 89. [Accessed 29 March 2024].
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