Basic theory of a class of linear functional differential equations with multiplication delay

Abstract

By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of linear pantograph equations. In particular, we get the complete results on the existence, uniqueness and non-uniqueness of the initial value problems at a general point for the kind of linear pantograph equations.

44 pages, no figure. This is a revised version of the third version of the paper. Some new results and proofs have been added

References in corpus (1)

• A new kind of functional differential equations

Cited by in corpus (2)

• The renormalization method from continuous to discrete dynamical systems: asymptotic solutions, reductions and invariant manifolds
• Exact Solutions and Reductions of Nonlinear Diffusion PDEs of Pantograph Type