On stability of nonlinear differential systems via cone-valued Liapunov function method

摘要

The notions of partial, relative and φ0-stability of ordinary differential equations (ODEs) are introduced in [E.P. Akpan, O. Akinyele, J. Math. Anal. Appl. 164 (1992) 307–324; V. Lakshmikantham, S. Leela, Differential and Integral Inequalities, vol. 1, Academic Press, New York, 1969]. In this paper, we extend these notions to new types of stability namely, φ0-relative and φ0-partial stability of ODEs using cone-valued Liapunov function method and comparison technique.