Annals of Functional Analysis

Stability on a cone in terms of two measures for differential equations with ``maxima''

Angel Dishliev and Snezhana Hristova

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Abstract

Stability in terms of two measures for nonlinear differential equations with ``maxima'' is studied. A special type of stability in terms of two measures is defined. The new type of stability generalizes some of the known in the literature. Sufficient conditions for the defined stability are obtained. Cone-valued continuous Lyapunov functions are applied. Method of Razumikhin as well as comparison method for scalar ordinary differential equations have been employed. The usefulness of the introduced definition and the obtained sufficient conditions is illustrated through an example.

Article information

Source
Ann. Funct. Anal., Volume 1, Number 1 (2010), 133-143.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900999

Digital Object Identifier
doi:10.15352/afa/1399900999

Mathematical Reviews number (MathSciNet)
MR2755465

Zentralblatt MATH identifier
1210.34100

Subjects
Primary: 47E99: None of the above, but in this section
Secondary: 34D20: Stability

Keywords
Lyapunov functions stability in two measures Razumikhin method differential equations with ``maxima''

Citation

Dishliev, Angel; Hristova, Snezhana. Stability on a cone in terms of two measures for differential equations with ``maxima''. Ann. Funct. Anal. 1 (2010), no. 1, 133--143. doi:10.15352/afa/1399900999. https://projecteuclid.org/euclid.afa/1399900999


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