Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay - Zhonghai Guo; Xiaoliang Zhou; Wu-Sheng Wang (Abstract and Applied Analysis)
We study the following second order mixed nonlinear impulsive differential equations with delay (r(t)Φα(x′(t)))′+p0(t)Φα(x(t))+∑i=1npi(t)Φβi(x(t-σ))=e(t), t≥t0, t≠τk,x(τk+)=akx(τk), x'(τk+)=bkx'(τk), k=1,2,…, where Φ*(u)=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.