Integral averages and oscillation of second order sublinear differential equations

Jelena V. Manojlović

Displaying similar documents to “Integral averages and oscillation of second order sublinear 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

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

A note on the oscillation of second order differential equations

Hishyar Kh. Abdullah (2004)

Czechoslovak Mathematical Journal

Similarity:

We give a sufficient condition for the oscillation of linear homogeneous second order differential equation $y^{''} + p (x) y^{'} + q (x) y = 0$ , where $p (x), q (x) \in C [α, \infty)$ and $α$ is positive real number.

Oscillation criteria for second order nonlinear perturbed differential equations.

Remili, M. (2010)

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

Similarity:

Disconjugacy and disfocality criteria for second order singular half-linear differential equations

Ondřej Došlý, Alexander Lomtatidze (1999)

Annales Polonici Mathematici

Similarity:

We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation $u^{''} = {p (t) | u |}^{α} {| u^{'} |}^{1 - α} s g n u + g (t) u^{'}$ , where α ∈ (0,1] and the functions $p, g \in L_{l o c} (a, b)$ are allowed to have singularities at the end points t = a, t = b of the interval under consideration.