Emphatic convergence and sequential solutions of generalized linear differential equations

0369691 - MÚ 2012 RIV GE eng J - Journal Article
Halas, Z. - Monteiro, G.A. - Tvrdý, Milan
Emphatic convergence and sequential solutions of generalized linear differential equations.
Memoirs on Differential Equations and Mathematical Physics. Roč. 54, - (2011), s. 27-49. ISSN 1512-0015
Institutional research plan: CEZ:AV0Z10190503
Keywords : generalized linear differential equation * continuous dependence on a parameter * Kurzweil-Stieljes integral
Subject RIV: BA - General Mathematics
http://www.rmi.ge/jeomj/memoirs/vol54/abs54-2.htm

This contribution deals with continuous dependence generalized linear differential equations in Banach space on a parameter. The authors continue in the previous research by M. Tvrdý and G. Monteiro, where the assumption of the uniform convergence of the kernels of the equations was the basic assumption. The contribution deals with the case when thise assumption is violated. Furthermore, a notion of a~sequential solution to generalized linear differential equations is introduced and Theorems on the existence and uniqueness of sequential solutions are proved and a comparison of solutions and sequential solutions is given, as well. The convergence effects occurring in this paper are, in some sense, very close to those described by Kurzweil and called by him emphatic convergence.
Permanent Link: http://hdl.handle.net/11104/0203698