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Š. Schwabik, M. Tvrdý, O. Vejvoda (1979)
Differential and integral equations : boundary value problems and adjoints
Differential Equations, Vol. 39, No. 3, 2003, pp. 344–352. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 3, 2003, pp. 320–327. Original Russian Text Copyright c 2003 by Lomtatidze, Hakl, P u za. ORDINARY DIFFERENTIAL EQUATIONS On the Periodic Boundary Value Problem for First-Order Functional-Di erential Equations A. G. Lomtatidze, R. Hakl, and B. P u za Masaryk University, Brno, Czech Republic Received August 6, 2002 1. STATEMENT OF THE PROBLEM AND BASIC NOTATION In the present paper, we consider the boundary value problem u (t)= `(u)(t)+ F (u)(t); (1:1) u(a)= u(b); (1:2) where ` : C ([a;b];R) ! L([a;b];R) is a linear bounded operator and F : C ([a;b];R) ! L([a;b];R) is a continuous operator, not necessarily linear. This problem, which is the subject of numerous studies, has long been attracting mathematicians' attention. Interesting results about its solvability can be found, e.g., in [1{11]. Nevertheless, problem (1.1), (1.2) has not been completely analyzed yet even for the linear case, in which Eq. (1.1) has the form u (t)= `(u)(t)+ g(t): (1:3) In a sense, we ll the gap. More precisely, new e ective criteria for the solvability and unique solvability of problems (1.3), (1.2) and (1.1), (1.2) are given
Differential Equations – Springer Journals
Published: Oct 5, 2004
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