Oscillation of third-order nonlinear differential equations. (English) Zbl 1209.34042

Baculíková, B.; Džurina, J.

Appl. Math. Lett. 24, No. 4, 466-470 (2011).

Summary: The objective of this work is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation
\[ [a(t)[x^{\prime \prime }(t)]^\gamma ]^{\prime} + q(t)f(x[\tau (t)])=0. \tag{E} \]
Applying suitable comparison theorems, we present new criteria for oscillation or certain asymptotic behaviors of nonoscillatory solutions of (E). The results obtained essentially improve and complement earlier ones.

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

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

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