Fixed points and stability in nonlinear neutral integro-differential equations with variable delay | Zendy

Imene Soualhia | Zendy; Abdelouaheb Ardjouni | Zendy; Ahcéne Djoudi | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Fixed points and stability in nonlinear neutral integro-differential equations with variable delay

Author(s) -

Imene Soualhia,

Abdelouaheb Ardjouni,

Ahcéne Djoudi

Publication year - 2014

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1404781s

Subject(s) - mathematics , fixed point theorem , fixed point , zero (linguistics) , nonlinear system , variable (mathematics) , differential equation , mathematical analysis , stability (learning theory) , metric space , exponential stability , pure mathematics , discrete mathematics , combinatorics , philosophy , linguistics , physics , quantum mechanics , machine learning , computer science

The nonlinear neutral integro-differential equation x′(t)=-∫_{t-τ(t)}^{t}a(t,s)g(x(s))ds+c(t)x′(t-τ(t)), with variable delays τ(t)≥0 is investigated. We find suitable conditions for τ, a, c and g so that for a given continuous initial function ψ a mapping P for the above equation can be defined on a carefully chosen complete metric space S_{ψ}⁰ in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient conditions. The obtained theorem improves and generalizes previous results due to Burton b2 , Becker and Burton b1 and Jin and Luo j1 .

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research