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

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.


34K10 Boundary value problems for functional-differential equations
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