... manyapplications such as mathematical finance, differential games, economics, and so on. Thesolvability of system (1.1), a n ontrivial generalization of s ystem (1.2), as far as I know,only a ... × [a, b]→X,andξ : X→X are nonlinear operators. {A( t) :a ≤ t ≤ b} is a family of linearclosed operators with adjoint operators A ∗(t) and generates a unique linear evolution system {U(t,s) :a ≤ ... (1.1)hasauniquesolutionon [a, b] under assumptions (A1 ), (A2 ),and (A3 ).Existence. ThesameargumentastheproofofTheorem 3.3.6 Boundary Value ProblemsCase 2 (α1= 0andα2> 0). Apply the var iation...