Oscillation criteria for a class of nonlinear vector delay-differential equations

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Oscillation criteria are obtained for a class of vector delay differential equation of the form

$$u''\left( t \right) + F_1 \left( {t,u\left( t \right),u\left( {g\left( t \right)} \right)} \right)u\left( t \right) + F_2 \left( {t,u\left( t \right),u\left( {g\left( t \right)} \right)} \right)u\left( {g\left( t \right)} \right) = 0$$

t≥0, u ε C2 ([0, ∞),R n), where F 1 and F 2 are continuous nonnegative valued functionals in [0, ∞)×R n×R n, and g is a continuous real valued function with g(t)≤t, g(t)→∞ as t→ ∞. A solution u: [0, ∞)→R n is called h-oscillatory in [0, ∞) whenever the scalar product [u(t), h] (│h│=1) has zeros in [a, ∞) with a arbitrary large. The method involves oscillatory behaviour of solutions of a nonlinear scalar delay differential inequality satisfied by h-nonoscillatory solutions of the above equation.


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Entrata in Redazione il 24 novembre 1976.

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Nababan, S. Oscillation criteria for a class of nonlinear vector delay-differential equations. Annali di Matematica 117, 55–66 (1978) doi:10.1007/BF02417884

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  • Differential Equation
  • Scalar Product
  • Oscillatory Behaviour
  • Delay Differential Equation
  • Differential Inequality