On an antiperiodic type boundary-value problem for first-order nonlinear functional-differential equations of non-Volterra’s type. (English) Zbl 1086.34536

Hakl, R.; Lomtatidze, A.; Šremr, J.

Nelinijni Kolyvannya 6, No. 4, 550-573 (2003).

The authors present sufficient conditions for solvability and unique solvability of the boundary value problem \[ u'(t) = F(u)(t),\qquad u(a) +\lambda u(b) = h(u), \] where \(F\: C([a,b];\mathbb{R})\to L([a,b];\mathbb{R})\) is a continuous operator satisfying the Carathéodory conditions, \(h\: C([a,b];\mathbb{R})\to \mathbb{R}\) is a continuous functional, and \(\lambda\in \mathbb{R}_+\). Some illustrative examples are given.

Reviewer: Julia A. Martynyuk (Kyïv)

MSC:

34K10

Boundary value problems for functional-differential equations

Keywords:

continuous operator; Carathéodory conditions; solvability of boundary value problem