Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. (English) Zbl 1023.34055

Bravyi, E.; Hakl, R.; Lomtatidze, A.

Czech. Math. J. 52, No. 3, 513-530 (2002).

Summary: In some sense nonimprovably sufficient conditions guaranteeing the unique solvability of the problem \[ u'(t)= \ell (u)(t)+q(t), \quad u(a)=c, \] where \(\ell : C(I, \mathbb{R}) \to L(I, \mathbb{R})\) is a linear bounded operator, \(q \in L(I, \mathbb{R})\), and \(c \in \mathbb{R}\), are established.

MSC:

34K06

Linear functional-differential equations

Keywords:

linear functional-differential equations; Cauchy problem; existence and uniqueness; differential inequalities

References:

[1]	N. V. Azbelev, V. P. Maksimov and L. F. Rakhmatullina: Introduction to the Theory of Functional Differential Equations. Nauka, Moscow, 1991. · Zbl 0725.34071
[2]	Sh. Gelashvili and I. Kiguradze: On multi-point boundary value problems for systems of functional differential and difference equations. Mem. Differential Equations Math. Phys. 5 (1995), 1-113. · Zbl 0902.34059
[3]	P. Hartman: Ordinary Differential Equations. John Wiley, New York, 1964. · Zbl 0125.32102
[4]	I. Kiguradze and B. Půža: On boundary value problems for systems of linear functional differential equations. Czechoslovak Math. J. 47 (1997), 341-373. · Zbl 0930.34047
[5]	Š. Schwabik, M. Tvrdý and O. Vejvoda: Differential and integral equations: boundary value problems and adjoints. Academia, Praha, 1979. · Zbl 0417.45001