Oscillation theorems for certain functional differential equations of higher order. (English) Zbl 1061.34047

Agarwal, R. P.; Grace, S. R.

Math. Comput. Modelling 39, No. 9-10, 1185-1194 (2004).

Summary: New oscillation criteria for \(n\)th-order functional-differential equations of the form \[ \left[\bigl(x^{(n-1)}(t)\bigr)^\alpha \right]'+ q(t)f \biggl(x\bigl[g(t)\bigr] \biggr)=0, \] when \(g(t)\) is a retarded argument, i.e., \(g(t)<t\) and \(g(t)\) is an advanced argument, i.e., \(g(t)>t\), are established.

MSC:

34K11

Oscillation theory of functional-differential equations

Keywords:

Oscillation; Nonoscillation; Comparison; Linearization; Half-linear; Functional

References:

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