Abstract
When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals. This makes the representing solution operators compact (or condensing), but, on the other hand, spaces equipped with such topologies become more complicated. This paper shows interesting applications that use the strength of continuation principles and also presents a possible extension of such continuation principles to partial differential inclusions.
Highlights
When solving boundary value problems on noncompact intervals, it is possible to use continuation principles
One cannot extend the Leray-Schauder type theorems, because of the obstructions brought by the topology of uniform convergence on compact subintervals
The main aim of this paper is to propose a modification of the continuation principle, originally given by Andres and Bader [1], to partial differential inclusions in Banach spaces and to present a nontrivial application of its usage
Summary
When solving boundary value problems on noncompact (in particular, on infinite) intervals, it is possible to use continuation principles. One cannot extend the Leray-Schauder type theorems, because of the obstructions brought by the topology of uniform convergence on compact subintervals (see [1, 2] or [6]). This topology makes the representing solution operators compact (or condensing) but, on the other hand, causes closed convex sets of certain type to have empty interiors. We recall a way to overcome this drawback by considering relatively open subsets of closed convex sets (see [2, 6]).
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