Oscillation criteria for first-order impulsive differential equations with positive and negative coefficients

Abstract

Some sufficient conditions are obtained for oscillation of all solutions of the first-order impulsive differential equation with positive and negative coefficientsOur results improve the known results in the literature.

Oscillation of Unforced Impulsive Neutral Delay Differential Equations of First Order

“…Not only our work gives an answer to the question (Q), but also deserve a more general work than that of [6], [8] and [15]. We note that (5), ( 6) and (7) are the special cases of (1).…”

“…and established sufficient conditions for oscillation of all solution of the systems (6) when p(t) ∈ P C([t 0 , ∞), R + ) only. In an another work [15], Shen and Zou have studied oscillation properties of first order impulsive neutral delay differential equations with positive and negative coefficients of the form…”

New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

“…In [3], the authors established some new oscillation criteria for first order impulsive neutral delay differential systems of the form (ν(λ) − p(λ)ν(λ − δ)) + q(λ)ν(λ − ς 1 ) − q 2 (λ)ν(λ − ς 2 ) = 0, ς ≥ δ > 0…”

Oscillatory criteria for third-order nonlinear difference equation with impulses

“…There has been a significant development in the theory of impulsive differential equations in the past several years, as various interesting results have been reported (see [1][2][3][4][5][6][7][8][9][10][11] etc., and the references therein). However, the development of the theory of impulsive difference equations is comparatively slow due to numerous theoretical and technical difficulties caused by their peculiarities [12][13][14][15].…”