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2010•Electronic journal of qualitative theory of differential equationsOpen access

Oscillation of third-order functional differential equations

Blanka Baculíková, Jozef Džurina

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Abstract

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation \begin{equation*}\label{E0} \left[a(t)\left[x''(t)\right]^{\gamma}\right]'+q(t)f(x\left[\tau(t)\right])=0. \tag{$E$} \end{equation*} Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of (\ref{E0}). Obtained results essentially improve and complement earlier ones. Various examples are considered to illustrate the main results.

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What this paper is about

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation \begin{equation*}\label{E0} \left[a(t)\left[x''(t)\right]^{\gamma}\right]'+q(t)f(x\left[\tau(t)\right])=0. \tag{$E$} \end{equation*} Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of (\ref{E0}). Obtained results essentially improve and complement earlier ones. Various examples are considered to illustrate the main results.

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Available abstract

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation \begin{equation*}\label{E0} \left[a(t)\left[x''(t)\right]^{\gamma}\right]'+q(t)f(x\left[\tau(t)\right])=0. \tag{$E$} \end{equation*} Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of (\ref{E0}). Obtained results essentially improve and complement earlier ones. Various examples are considered to illustrate the main results.

Key concepts: Oscillation (cell signaling), Mathematics, Order (exchange), Differential equation, Functional differential equation, Third order, Differential (mechanical device), Applied mathematics

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