Oscillatory and asymptotic behavior of solutions for second-order mixed nonlinear integro-dynamic equations with maxima on time scales | Zendy

H. A. Agwa | Zendy; Mokhtar A. Abdel Naby | Zendy; Heba M. Arafa | Zendy

Open Access

Oscillatory and asymptotic behavior of solutions for second-order mixed nonlinear integro-dynamic equations with maxima on time scales

Author(s) -

H. A. Agwa,

Mokhtar A. Abdel Naby,

Heba M. Arafa

Publication year - 2019

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/fil1910907a

Subject(s) - mathematics , maxima , dynamic equation , order (exchange) , nonlinear system , mathematical physics , mathematical analysis , pure mathematics , physics , quantum mechanics , art , finance , performance art , economics , art history

This paper is concerned with the oscillatory and asymptotic behavior for solutions of the following second-order mixed nonlinear integro-dynamic equations with maxima on time scales (r(t)(z?(t))?)? + ?t0 a(t,s) f(s, x(s))?s + ?n,i=1 qi(t) max s?[?i(t),?i(t)] x?(s) = 0, where z(t) = x(t) + p1(t)x(?1(t)) + p2(t)x(?2(t)), t ? [0,+?)T. The oscillatory behavior of this equation hasn?t been discussed before, also our results improve and extend some results established by Grace et al. [2] and [8].

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