On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type

Title:

On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type

Creator:

Bravyi, E., Hakl, Robert, and Lomtatidze, Alexander

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1024ea52-c9a5-4b71-9700-1231c24613bf
uuid:1024ea52-c9a5-4b71-9700-1231c24613bf

Subject:

nonlinear functional differential equation, initial value problem, and non–Volterra’s type operator

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

On the segment $I=[a,b]$ consider the problem \[ u^{\prime }(t)=f(u)(t) , \quad u(a)=c, \] where $f\:C(I,\mathbb{R})\rightarrow L(I,\mathbb{R})$ is a continuous, in general nonlinear operator satisfying Carathéodory condition, and $c\in \mathbb{R}$. The effective sufficient conditions guaranteeing the solvability and unique solvability of the considered problem are established. Examples verifying the optimality of obtained results are given, as well.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

673-690

Source:

Czechoslovak Mathematical Journal | 2002 Volume:52 | Number:4

Harvested from:

CDK

Metadata only:

false