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

On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type. (English) Zbl 1023.34054

Czech. Math. J. 52, No. 4, 673-690 (2002).
Summary: On the segment \(I=[a,b]\) consider the problem \(u'(t)=f(u)(t), \quad u(a)=c\), where \(f: C(I,\mathbb{R}) \to L (I,\mathbb{R})\) is a continuous, in general nonlinear operator satisfying Carathéodory condition, and \(c \in \mathbb{R}\). Sufficient conditions guaranteeing the solvability and unique solvability of the considered problem are established. Examples verifying the optimality of obtained results are given, too.

Cited in 8 Documents

MSC:

34K05 General theory of functional-differential equations

Keywords:

nonlinear functional-differential equation; initial value problem; non-Volterra-type operator
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\textit{E. Bravyi} et al., Czech. Math. J. 52, No. 4, 673--690 (2002; Zbl 1023.34054)
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References:

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