Volterra Integral And Functional Equations

By M. Abend. 2016

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Affine Volterra processes (2017, methodology): “If F is a function on R+, we write K ∗ F = K ∗ (Fdt), that is, (K ∗ F )(t) = ∫ t 0 K(t− s)F (s)ds. (2.2) Further details can be found in Gripenberg et al. (1990), see in particular Definitions 2.2.1 and 3.2.1, as well as Theorems 2.2.2 and 3.6.1 for a number of properties of convolutions.”
Hyers‐Ulam‐Rassias stability of nonlinear integral equations through the Bielecki metric (2018, background): “a σðτÞdτ≤ησðxÞ; (21) for all x∈ [a, b].”
Fundamental solutions and decay of fully non-local problems (2018, background): “There exists a substantial amount of work on such abstract Volterra and integro-differential equations since the 1970s, in particular on existence and uniqueness, regularity, and long-time behavior of solutions, see, for instance, [8, 14, 31, 32], and the monograph [25].”