Stability criteria for impulsive differential equations in terms of two measures.

*(English)*Zbl 0688.34031Stability theory of impulsive differential systems with fixed moments of impulse effects is discussed. The stability concepts are treated in terms of two measures, that gives rise to unifying a variety of stability results found in the literature. The theorems are proved by the theory of impulsive differential inequalities and the direct method.

Reviewer: L.Hatvani

##### MSC:

34D20 | Stability of solutions to ordinary differential equations |

##### Keywords:

impulsive differential systems with fixed moments of impulse effects; impulsive differential inequalities
PDF
BibTeX
XML
Cite

\textit{V. Lakshmikantham} and \textit{X. Liu}, J. Math. Anal. Appl. 137, No. 2, 591--604 (1989; Zbl 0688.34031)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Bainov, D.D; Simeonov, P.S, The second method of Lyapunov for systems with an impulse effect, Tamkang J. math., 16, 19-40, (1985) · Zbl 0641.34051 |

[2] | Bainov, D.D; Simenov, P.S, Stability with respect to part of the variables in systems with impulsive effect, J. math. anal. appl., 117, 247-263, (1986) · Zbl 0588.34044 |

[3] | {\scD. D. Bainov, and G. K. Kulev}, Second method of Lyapunov and comparison principle for systems with impulse effect, to appear. · Zbl 0711.34071 |

[4] | {\scD. D. Bainov, V. Lakshmikantham, and P. S. Simeonov}, Theory of impulsive differential equations, to appear. · Zbl 0949.34002 |

[5] | Gurgula, S.I, Investigation of the stability of solutions of impulse systems by Lyapunov’s second method, Ukrainian math. J., 1, 100-103, (1982) · Zbl 0508.34038 |

[6] | {\scV. Lakshmikantham and Xinzhi Liu}, Perturbing families of Lyapunov functions and stability in terms of two measures, J. Math. Anal. Appl., to appear. · Zbl 0669.34056 |

[7] | Perestyuk, N.A; Samoilenko, A.M, Differential equations with impulsive effect, (1987), Central Publishers Kiev · Zbl 0837.34003 |

[8] | {\scR. Pirapakaran}, Impulsive integral inequalities of Gronwall-Bihari type, to appear. · Zbl 0718.34012 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.