On the Existence of Solutions for Boundary Value Problems in Banach Spaces

Authors : Hero SALAHİFARD, S Mansour VAEZPOUR, Abdolrahman RAZANİ

Pages : 0-0

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Publication Date : 2015-11-01

Article Type : Research Paper

Abstract :In this paper, by applying the theory of condensing multimaps and the topological degree, we deal with the existence of solutions for boundary value problems with second order differential inclusions in different cases where the underlying space is a Banach space. Indeed, we investigate the existence of solutions for the BVP insert ignore into journalissuearticles values( x ′′insert ignore into journalissuearticles values(t); ∈ Finsert ignore into journalissuearticles values(t, xinsert ignore into journalissuearticles values(t);); t ∈ I = [0,1], xinsert ignore into journalissuearticles values(0); = xinsert ignore into journalissuearticles values(1); = 0, where X is a real Banach space and the multifunction F : I ×X ⊸ Kinsert ignore into journalissuearticles values(X);, in one case, has convex values and in another case has non-convex values insert ignore into journalissuearticles values(Kinsert ignore into journalissuearticles values(X); denotes compact subsets of X);. Moreover, some results on the existence of solutions for the extended version of BVP insert ignore into journalissuearticles values( u ′′insert ignore into journalissuearticles values(t); ∈ Qinsert ignore into journalissuearticles values(u); t ∈ I, uinsert ignore into journalissuearticles values(0); = uinsert ignore into journalissuearticles values(1); = 0, are presented, where Q :Cinsert ignore into journalissuearticles values(I,X); ⊸Cinsert ignore into journalissuearticles values(L 2 ); is a multimap satisfying some appropriate conditions. Finally, we show how the results can be used to study periodic feedback control systems
Keywords : Boundary Value Problems, Condensing map, Feedback control systems, Topological degree