Open AccessOscillatory and asymptotic behavior of solutions for second-order mixed nonlinear integro-dynamic equations with maxima on time scales
Author(s) -
Hassan Agwa Ahmed,
Mokhtar Naby Ahmed,
Heba Arafa Mohamed
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].