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On a Boundary-Value Problem of Antiperiodic Type for First-Order Nonlinear Functional Differential Equations of Non-Volterra Type
Authors:Hakl  R.  Lomtatidze  A.  Šremr  J.
Affiliation:(1) Mathematical Institute, Czech Academy of Sciences, Brno, Czech Republic;(2) Masaryk University, Brno, Czech Republic
Abstract:We establish unimprovable (in a certain sense) sufficient conditions for the solvability and unique solvability of the boundary-value problem

$$u'left( t right) = Fleft( u right)left( t right),uleft( a right) + lambda uleft( b right) = hleft( u right),$$
where 
$$F:Cleft( {left[ {a,b} right];R} right) to Lleft( {left[ {a,b} right];R} right)$$
is a continuous operator satisfying the Carathéodory conditions, h: C([a, b]; R) rarr R is a continuous functional, and lambda isin R+.
Keywords:
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