Opuscula Math. 29, no. 1 (2009), 69-79
Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations
Abstract. The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.
Keywords: functional differential equations, comparison methods, estimates of the Perron type.
Mathematics Subject Classification: 35R10, 35L45.
- Received: 2008-05-06.
- Revised: 2008-06-20.
- Accepted: 2008-06-22.