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Oscillation of even order nonlinear functional differential equations with deviating arguments. (English) Zbl 0704.34076
The functional differential equation (1)L n x(t)+q(t)f(x[g(t)])=0, n is even, is considered. In (1) L 0 x(t)=x(t), L k x(t)=(1/a k (t))(L k-1 x(t)) , 1kn ( =d/dt), a n =1, a i :[t 0 ,)(0,), i=1,2,···,n-1, q,g: [t 0 ,), f: are continuous, q(t)0 are not identically zero on any ray of the form [t * ,) for some t * t 0 and lim t g(t)=. A solution of equation (1) is called oscillatory if it has arbitrary large zeros; otherwise it is called non- oscillatory. Equation (1) is said to be oscillatory if all its solutions are oscillatory. A new oscillation criterion for equation (1) is established.
Reviewer: B.Cheshankov
34K99Functional-differential equations
34A34Nonlinear ODE and systems, general
34C15Nonlinear oscillations, coupled oscillators (ODE)