Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

Abstract EN

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.