A remark on the half-linear extension of the Hartman-Wintner theorem.

Došlý, Ondřej

Displaying similar documents to “A remark on the half-linear extension of the Hartman-Wintner theorem.”

Hartman-Wintner type criteria for half-linear second order differential equations

Zuzana Pátíková (2007)

Mathematica Bohemica

Similarity:

We establish Hartman-Wintner type criteria for the half-linear second order differential equation ${(r (t) Φ (x^{'}))}^{'} + c (t) Φ (x) = 0, Φ (x) = {| x |}^{p - 2} x, p > 1,$ where this equation is viewed as a perturbation of another equation of the same form.

Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments

Roman Koplatadze, N. L. Partsvania, Ioannis P. Stavroulakis (2003)

Archivum Mathematicum

Similarity:

Sufficient conditions are established for the oscillation of proper solutions of the system $\begin{matrix} u_{1}^{'} (t) & = p (t) u_{2} (σ (t)), \\ u_{2}^{'} (t) & = - q (t) u_{1} (τ (t)), \end{matrix}$ where $p, q : R_{+} \to R_{+}$ are locally summable functions, while $τ$ and $σ : R_{+} \to R_{+}$ are continuous and continuously differentiable functions, respectively, and $lim_{t \to + \infty} τ (t) = + \infty$ , $lim_{t \to + \infty} σ (t) = + \infty$ .

Conjugacy and disconjugacy criteria for second order linear ordinary differential equations

T. Chantladze, Alexander Lomtatidze, Douglas Ugulava (2000)

Archivum Mathematicum

Similarity:

Conjugacy and disconjugacy criteria are established for the equation $u^{''} + p (t) u = 0,$ where $p :] - \infty, + \infty [\to] - \infty, + \infty [$ is a locally summable function.

Oscillation criteria for second order nonlinear perturbed differential equations.

Remili, M. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Similarity:

Oscillation criteria for second order self-adjoint matrix differential equations

N. Parhi, P. Praharaj (1999)

Annales Polonici Mathematici

Similarity:

Some results concerning oscillation of second order self-adjoint matrix differential equations are obtained. These may be regarded as a generalization of results for the corresponding scalar equations.