Approximation of solutions to history-valued neutral functional differential equations

Approximation of solutions to history-valued neutral functional differential equations

K e y w o r d s N e u t r a l functional differential equation, Analytic semigroup, Mild solution, FaedoGalerkin approximation. 1. I N T R O D U C T I O N Let H be a separable Hilbert space and 0 < T, T < ec. For 0 < t < T, Ct := C([-~-, t]; H) be the Banach space of all continuous functions from l--T, t] into H endowed with the supremum norm, Ilullt := sup I lu(s) l l , u • Ct, (1.1) -r<_s<t w...

Existence and continuous dependence for fractional neutral functional differential equations

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

Existence of Positive Periodic Solutions for Neutral Functional Differential Equations

We find sufficient conditions for the existence of positive periodic solutions of two kinds of neutral differential equations. Using Krasnoselskii’s fixed-point theorem in cones, we obtain results that extend and improve previous results. These results are useful mostly when applied to neutral equations with delay in bio-mathematics.

Oscillation of Solutions for Odd-order Neutral Functional Differential Equations

In this article, we establish oscillation criteria for all solutions to the neutral differential equations [x(t)± ax(t± h)± bx(t± g)] = p Z d

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations