Opuscula Math. 34, no. 2 (2014), 327-338
Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay
Abstract. We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.
Keywords: successive approximations, Darboux problem, infinite delay.
Mathematics Subject Classification: 35R10.
- Received: 2012-10-25.
- Revised: 2014-02-09.
- Accepted: 2014-02-21.