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Emphatic convergence and sequential solutions of generalized linear differential equations

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    0369691 - MU-W 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
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