On the analytical computation of functional solutions associated with first order differential systems. (English) Zbl 1060.35010

Iftimie, B.; Vârsan, C.

Math. Rep., Bucur. 4(54), No. 1, 71-85 (2002).

Summary: By using an abstract form of the Cauchy-Kovalewska theorem (the Ovsyannikov theorem), we get the existence of the unique solution to first order differential equations with parameters in the space of continuous functions. We analyze the analytical dependence of the solution with respect to the function-parameter provided the right hand side \(f(x,p(\cdot))\) depends analytically on \(p\).

MSC:

35B20	Perturbations in context of PDEs
39B72	Systems of functional equations and inequalities

Keywords:

first order functional differential equation; analytic solution