Smooth solution of an initial value problem for a mixed-type differential difference equation

Abstract:

In this paper, we show the construction of the solution to the mixed type differential difference equation: x′(t) = Ax(t + a) + Bx(t - a) + Cx(t), where A,B,C ∈ ℂ \ {0}, a > 0 and t ∈ ℝ. We use a step derivative method and a certain condition on the initial function φ ∈ C∞[-a, a] to assure the existence, uniqueness and smoothness of the solution in ℝ.

Año de publicación:

2015

Keywords:

• Differential difference equations
• Initial value problems

Fuente:

scopus