Oscillation of First Order Delay Differential Equations

Abstract

Some new oscillation criteria for the first-order delay differential equation

Oscillation for First Order Superlinear Delay Differential Equations

“…We refer to the monographs [2,3,5] and recent papers [1, 4, 6-9, [11][12][13]. A classical result is (see [2,3]) that every solution of (3) oscillates if…”

Oscillation of first order delay differential equations with distributed delay

“…Integral conditions like (1.4) and (1.5) have been employed extensively in the study of the oscillatory properties of various functional differential equations. When the limit lim t →∞ t t −τ p(s) ds does not exist, there is an obvious gap between 1/e and 1; in the recent literature [9,11,[16][17][18][19][20][21] …”

“…In the recent literature, there have been numerous results on the oscillation for delay differential equation with discrete delays; see, for example, papers [1,4,[8][9][10][11][12][13][14][15][17][18][19][20][21][22][23], books [5,7,16] and references therein. But only a relatively few publications on oscillation for delay differential equation with distributed delay are found; see [2,3] and references cited ✩ This work was supported by NNSF of China.…”

Linearized oscillation of odd order nonlinear neutral delay differential equations (I)

“…(1.2) In the past 15 years, the linearized oscillation theory for nonlinear neutral delay differential equations has been extensively developed, for example, see [1][2][3][4][5][6][7][8][9][10][11][12][13]. Linearization is an important method to deal with nonlinear mathematical problems.…”