Asymptotic behaviour of the equation \(\dot z=G(t,z)[h(z)+g(t,z)]\). (English) Zbl 0702.34042

Kalas, Josef

Arch. Math., Brno 25, No. 4, 195-206 (1989).

Summary: Asymptotic properties of the solutions of an equation \(\dot z=G(t,z)[h(z)+g(t,z)]\) with real-valued function G and complex-valued functions h, g are studied. The technique of the proofs of results is based on the modified Lyapunov function method. The results are applied to the generalized Riccati equation \(\dot z=q(t,z)-p(t)z^ 2\).

MSC:

34D05	Asymptotic properties of solutions to ordinary differential equations
34D20	Stability of solutions to ordinary differential equations

Keywords:

modified Lyapunov function method; Riccati equation