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Keywords:
linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities
linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities
Summary:
Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t), \qquad u(a)=c, \] where $\ell \:C(I,\mathbb R)\rightarrow L(I,\mathbb R)$ is a linear bounded operator, $q\in L(I,\mathbb R)$, and $c\in \mathbb R$, are established.
References:
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[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. MR 1415806
[3] P. Hartman: Ordinary Differential Equations. John Wiley, New York, 1964. MR 0171038 | 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. DOI 10.1023/A:1022829931363 | MR 1452425
[5] Š. Schwabik, M. Tvrdý and O. Vejvoda: Differential and integral equations: boundary value problems and adjoints. Academia, Praha, 1979. MR 0542283
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