Some new trends in Lyapunov's direct method
WCNA '92 Proceedings of the first world congress on World congress of nonlinear analysts '92, volume II
Recent trends in the theory of nonlinear functional differential equations
WCNA '92 Proceedings of the first world congress on World congress of nonlinear analysts '92, volume II
Existence theory for nonlinear Volterra integrodifferential and integral equations
Nonlinear Analysis: Theory, Methods & Applications
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The aim of this paper is to summarize some of the basic concepts and results, available in the mathematical (and partially) or engineering literature, related to functional or differential functional equations with abstract Volterra operators (causal or nonanticipative, as these operators are called in the engineering literature). Equations such as x(t) = (Vx)(t), x'(t) = (Vx)(t), or (Vx)(t) = (Wx)(t), where V and W are causal operators, are dealt with. Existence, uniqueness of solutions in various function spaces are established. Further results on boundary value problems, stability, or asymptotic behavior are considered. Connections with classical types of functional equations are emphasized. Some applications are briefly indicated.