On stability of nonlinear systems of ordinary differential equations

The notions of φ 0-stability, ( h 0, h)-stability integral and eventual stability of nonlinear systems of ordinary differential equations (ODE's) are introduced. Our aim in this paper is to improve and extend these notions to new types of stability namely, φ 0– L p -stability, ( h 0, h)-integra...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 113; no. 2; pp. 175 - 198
Main Authors El-Sheikh, M.M.A., Soliman, A.A., Abd Alla, M.H.
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 15.07.2000
Elsevier
Subjects
Exact sciences and technology
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
Stability
Integral stability
Differential equation
Perturbation
Non linear system
Monotonicity
Equistability
Equation system
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Summary:The notions of φ 0-stability, ( h 0, h)-stability integral and eventual stability of nonlinear systems of ordinary differential equations (ODE's) are introduced. Our aim in this paper is to improve and extend these notions to new types of stability namely, φ 0– L p -stability, ( h 0, h)-integral stability and ( h 0, h)-eventual stability of systems of ODE's, respectively, and given some criteria. Our technique depends on Liapunov direct method.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(99)00082-X