Conjugacy and disconjugacy criteria for second order linear ordinary differential equations

T. Chantladze; Alexander Lomtatidze; Douglas Ugulava

Displaying similar documents to “Conjugacy and disconjugacy criteria for second order linear ordinary differential equations”

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

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

Archivum Mathematicum

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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 $lim_{t \to + \infty} τ (t) = + \infty$ , $lim_{t \to + \infty} σ (t) = + \infty$ .

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

Zuzana Pátíková (2007)

Mathematica Bohemica

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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.

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

Došlý, Ondřej (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators

Jiří Šremr (2007)

Mathematica Bohemica

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We establish new efficient conditions sufficient for the unique solvability of the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators.

On positive solutions of a class of second order nonlinear differential equations on the halfline

Svatoslav Staněk (1995)

Annales Polonici Mathematici

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The differential equation of the form ${(q (t) k (u) {(u^{'})}^{a})}^{'} = f (t) h (u) u^{'}$ , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.