Oscillation of third-order functional differential equations. (English) Zbl 1211.34077

Baculikova, B.; Dzurina, J.

Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 43, 10 p. (2010).

Summary: The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation
\[ \left[a(t)\left[x''(t)\right]^{\gamma}\right]'+q(t)f(x\left[\tau(t)\right])=0. \tag{1} \]
Applying suitable comparison theorems, we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of (1). The obtained results essentially improve and complement earlier ones. Various examples are considered to illustrate the main results.

MSC:

34K11

Oscillation theory of functional-differential equations

Keywords:

third-order functional differential equations; oscillation; nonoscillation; comparison theorem