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Emphatic convergence and sequential solutions of generalized linear differential equations
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SYSNO ASEP 0369691 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title Emphatic convergence and sequential solutions of generalized linear differential equations Author(s) Halas, Z. (CZ)
Monteiro, G.A. (BR)
Tvrdý, Milan (MU-W) RID, ORCID, SAISource Title Memoirs on Differential Equations and Mathematical Physics - ISSN 1512-0015
Roč. 54, - (2011), s. 27-49Number of pages 23 s. Language eng - English Country GE - Georgia Keywords generalized linear differential equation ; continuous dependence on a parameter ; Kurzweil-Stieljes integral Subject RIV BA - General Mathematics CEZ AV0Z10190503 - MU-W (2005-2011) Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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