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Zbl 1210.34100
Dishliev, Angel; Hristova, Snezhana
Stability on a cone in terms of two measures for differential equations with ``maxima''. (English)
[J] Ann. Funct. Anal. AFA 1, No. 1, 133-143, electronic only (2010). ISSN 2008-8752/e

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 ones in the literature. Sufficient conditions for the defined stability are obtained. Cone-valued continuous Lyapunov functions are applied. The method of Razumikhin as well as a comparison method for scalar ordinary differential equations are employed. The usefulness of the introduced definition and the obtained sufficient conditions is illustrated through an example.
[Alexander O. Ignatyev (Donetsk)]

MSC 2000:: *34K20 Stability theory of functional-differential equations

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

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