Abstract
LetB be a Banach space ofR n valued continuous functions on [0, ∞) withf∈B. Consider the nonlinear Volterra integral equation (*)x(t)+ ∫ to K(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionx∈B to (*) for eachf ∈B with ∥f∥B sufficiently small. Moreover, there is a constantM>0 independent off with ≤M∥f∥B.
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Part of this work was done while the author was visiting at Wright State University.
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Ward, J.R. The existence of solutions, stability, and linearization of volterra systems. Math. Systems Theory 11, 177–197 (1977). https://doi.org/10.1007/BF01768476
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DOI: https://doi.org/10.1007/BF01768476