Stability of linear differential equations with a distributed delay | Zendy

Leonid Berezansky | Zendy; Elena Braverman | Zendy

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Stability of linear differential equations with a distributed delay

Author(s) -

Leonid Berezansky,

Elena Braverman

Publication year - 2011

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2011.10.1361

Subject(s) - differential equation , delay differential equation , mathematics , scalar (mathematics) , mathematical analysis , stability (learning theory) , physics , mathematical physics , geometry , computer science , machine learning

We present some new stability results for the scalar linear equation with a distributed delay $\dot{x}(t) + \sum_{k=1}^m \int_{h_k(t)}^t x(s) d_s R_k(t,s) =0, h_k(t)\leq t,$ su$p_{t\geq 0}(t-h_k(t))<\infty,$ where the functions involved in the equation are not required to be continuous. The results are applied to integro-differential equations, equations with several concentrated delays and equations of a mixed type.

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