Smoothness of solutions of conjugate boundary-value problems on a measure chain

Abstract

In this paper we consider the n-th order $Delta$-differential equation (often refered to as a differential equation on a measure chain) $$u^{Delta_n}(t) = f(t, u(sigma(t)),dots, u^{Delta_{n-1}}(sigma(t)))$$ satisfying n-point conjugate boundary conditions. We show that solutions depend continuously and smoothly on the boundary values.

Keywords

• Measure chain
• initial-value problem
• boundary-value problem.