Under Lipschitz continuity and a contraction condition, a second-order Volterra integrodifferential equation with nonlocal and boundary conditions has a unique solution that depends continuously on its data.
Byszewski, Continuous dependence of mild solutions, on initial n onlocal data, of the nonlocal semilinear evolution Cauchy problems, Czasopismo Technicz ne 9 (2017), 151–158
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Analysis of Volterra Integrodifferential Equations with Nonlocal and Boundary Conditions via Picard Operator
Under Lipschitz continuity and a contraction condition, a second-order Volterra integrodifferential equation with nonlocal and boundary conditions has a unique solution that depends continuously on its data.