Differential and Integral Equations

Oscillatory behavior near blow-up of the solutions to some second-order nonlinear ODE

Faouzia Aloui

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Abstract

We study the oscillation properties of solutions to the nonlinear scalar second-order ODE \begin{equation} u''(t)+\vert u(t) \vert ^{\beta}u(t)+g(u'(t))=0,\quad t\leq0, \end{equation} where $\beta$ is a positive constant and $g:\mathbf{R}\rightarrow \mathbf{R}$ is an increasing and locally Lipschitz function behaving globally like $\vert v \vert^{\alpha}v$, $\alpha>0.$

Article information

Source
Differential Integral Equations, Volume 25, Number 7/8 (2012), 719-730.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012660

Mathematical Reviews number (MathSciNet)
MR2975692

Zentralblatt MATH identifier
1265.34124

Subjects
Primary: 34C100 34C15: Nonlinear oscillations, coupled oscillators 34D05: Asymptotic properties 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]

Citation

Aloui, Faouzia. Oscillatory behavior near blow-up of the solutions to some second-order nonlinear ODE. Differential Integral Equations 25 (2012), no. 7/8, 719--730. https://projecteuclid.org/euclid.die/1356012660


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