On a boundary value problem for first-order scalar functional differential equations Original Research Article

Nonimprovable effective sufficient conditions for solvability and unique solvability of the boundary value problem u′(t)=F(u)(t),u(a)=h(u), where F:C([a,b];R)→L([a,b];R) is a continuous operator satisfying the Carathèodory condition and h:C([a,b];R)→R is a continuous functional, are established.