On the Cauchy problem for linear PDEs with retarded arguments at derivatives
Tom 113 / 2015
Annales Polonici Mathematici 113 (2015), 269-282 MSC: 35A01, 35G10, 35R10. DOI: 10.4064/ap113-3-4
We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.