Neutral delay differential equations with positive and negative coefficients

Existence of positive solutions for a neutral differential equation with positive and negative coefficients

“…(1) have been investigated by several authors; see for example [1][2][3][4][5][6][7][8][9][10][11][12]. The first results for oscillation of Eq.…”

“…Luo et al [6], Tang and Yu [9] obtained some results for the oscillatory and nonoscillatory behaviors of Eq. (1) which do not require condition (3). They used the following condition:…”

Oscillation Criteria for First Order Neutral Differential Equations with Positive and Negative Coefficients

“…The oscillation of Eq. 1 has recently been investigated by many authors w x w x w x including Chuanxi and Ladas 2 , Farrall et al 4 Ž . Ž .…”

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

“…There are many good results on the oscillation of (1.3), see for example [2,3,7,9,10], but all of them consider the three cases when…”

“…However, the theory of impulsive functional differential equations is developing comparatively slowly due to numerous theoretical and technical difficulties caused by their peculiarities. In particular, to the best of our knowledge, there is little in the way of results for the oscillation of impulsive delay differential equations of neutral type despite the extensive development of the oscillatory and nonoscillatory properties of neutral differential equations without impulses (for example, see [5,6,2,3,7,[9][10][11][12]). In this paper, we consider the oscillation of all solutions of the following impulsive neutral delay differential equations with positive and negative coefficients, (1.1) and (1.2) reduce to the first-order neutral delay differential equations with positive and negative coefficients…”