Nonuniqueness theorem for a singular Cauchy problem. (English) Zbl 0970.34005

Kalas, Josef

Georgian Math. J. 7, No. 2, 317-327 (2000).

A general nonuniqueness criterion for the nonsingular Cauchy problem obtained by the present author elsewhere [Dyn. Contin. Discrete Impulsive Syst. 3, No. 1, 97-111 (1997; Zbl 0870.34006)] is extended to a singular case. Since the scalar function has been replaced by the vector Lyapunov function, the results apply to wider classes of differential equations. A number of illustrative examples is considered.

Reviewer: Yuri V.Rogovchenko (Famagusta)

MSC:

34A12

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

Keywords:

uniqueness and nonuniqueness of solutions; singular Cauchy problem; Lyapunov functions

Citations:

Zbl 0870.34006