Generalized Cauchy problems for hyperbolic functional differential systems
Volume 110 / 2014
Annales Polonici Mathematici 110 (2014), 33-53 MSC: 35R10, 35F25, 35A05. DOI: 10.4064/ap110-1-4
A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.