Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Authors: Bravyi E.¹; Hakl R.²; Lomtatidze A.³

Source: Czechoslovak Mathematical Journal, Volume 52, Number 3, September 2002 , pp. 513-530(18)

Publisher: Springer

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Abstract:

Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem u^\prime(t)=\ell(u)(t)+q(t), \quad u(a)=c,

where \ell: \ C(I, {\Bbb R}) \rightarrow L(I, {\Bbb R}) is a linear bounded operator, q \in L(I,{\Bbb R}), and c \in {\Bbb R} are established.

Keywords: linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematical Analysis, Perm State Technical University, Komsomolsky str. 29a, 614000 Perm, Russia, bravyi@pi.ccl.ru 2: Department of Mathematical Analysis, Masaryk University, Janá ccaron kovo nám. 2a, 662 95 Brno, Czech Republic, hakl@math.muni.cz kovo nám. 2a, 662 95 Brno, Czech Republic, hakl@math.muni.cz "> 3: Department of Mathematical Analysis, Masaryk University, Janá ccaron kovo nám. 2a, 662 95 Brno, Czech Republic, bacho@math.muni.czkovo nám. 2a, 662 95 Brno, Czech Republic, bacho@math.muni.cz">