Acyclicity of the solution set of two-point boundary value problems for second order multivalued differential equations
Classical Analysis and ODEs
2019-01-03 v1
Abstract
The topological and geometrical structure of the set of solutions of two-point boundary value problems for second order differential inclusions in Banach spaces is investigated. It is shown that under the Carath\'eodory-type assumptions the solution set of the periodic boundary value problem is nonempty compact acyclic in the space of continuously differentiable functions as well as in the Bochner-Sobolev space endowed with the weak topology. The proof relies heavily on the accretivity of the right-hand side of differential inclusion. The Lipschitz case is treated separately. As one might expect the solution set is, in this case, an absolute retract.
Cite
@article{arxiv.1901.00467,
title = {Acyclicity of the solution set of two-point boundary value problems for second order multivalued differential equations},
author = {Radosław Pietkun},
journal= {arXiv preprint arXiv:1901.00467},
year = {2019}
}