On oscillatory and asymptotic properties of solutions of certain nonlinear third order differential equations. (English) Zbl 0945.34021

Gera, M.; Graef, J. R.; Greguš, M.

Nonlinear Anal., Theory Methods Appl. 32, No. 3, 417-425 (1998).

The authors investigate oscillatory and asymptotic properties of solutions to the third-order nonlinear differential equation \[ x'''+p(t,x,x',x'')x''+q(t,x,x',x'')x'+r(t,x,x',x'')x=f(t,x,x',x''), \tag{*} \] where \(p,q,r,f\) are continuous functions on \((\alpha,\infty)\times \mathbb{R}^n\), \(\alpha\in \mathbb{R}\). Using the linearization technique combined with a comparison principle conditions on the functions \(p,q,r,f\) are given which guarantee that every solution to (*) with one zero is oscillatory. Asymptotic properties of nonoscillatory solutions are studied, too.

Reviewer: Ondřej Došlý (Brno)

MSC:

34C10

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

Keywords:

asymptotic behavior; disconjugate; nonlinear; oscillation; third order

References:

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