Asymptotic Behavior of Solutions of Nonlinear Volterra Equations with Completely Positive Kernels

𝐶^{𝛼}-classical solutions for abstract non-autonomous integro-differential equations

“…In the theory developed in [9,18], the internal energy and the heat flux are described as functionals of u(·) and u x (·). The next system (see for instance [2,3,16,19]) has been frequently used to describe this phenomena: In this system, (t, x) ∈ R × Ω, Ω ⊂ R n is an open bounded set with smooth boundary ∂Ω, y ∈ ∂Ω, u(t, x) represents the temperature in x at the time t, c is a physical constant and k i : R → R, i = 1, 2, are the internal energy and the heat flux …”

On abstract Volterra equations in Banach spaces with completely positive kernels

“…In some recent works [4], [3] , [5], [1] we considered the abstract Volterra equation: t t u(t) + f b(t-s)Au(s)ds : u 0 + ~ b(t-s)g(s)ds, t ~ 0 (V) 0 0 1 A is a linear or nonlinear where b is a real kernel in Lloc, m-accretive operator in a real Banach space X, u 0 • X and g • LllocQR+'X)' . Such equation has been previously studied by several authors [8], [9], [10], [2], [13], [ii], [6], [14].…”

Existence results for abstract neutral functional differential equations

“…In the theory developed in [14,23], the internal energy and the heat flux are described as functionals of and . The next system (see [7,8,9,22]) has been frequently used to describe this phenomena:…”