On a boundary value problem associated with some difference-differential equations

Abstract

The existence and uniqueness of the continuous solution of the following boundary value problem is discussed.

where d₀=g(0), d₁=h(0) and k(0)=k’(0)=0. This provides the solution to the system of equations of the type

In the special case f(t)=t−b, φ(t)=0, g(t)=t^γ and h(t)=(γ+1)⁻¹t^γ+1, γ>0, the solution y(x,t) of the above boundary value problem is the generating function for the system of polynomials developed by Soni and Sleeman.