Third Order Linear Differential Equations with Periodic Coefficients

THIRD ORDER LINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS i

The third order linear differential equation Ly = y'" + p2(t)y" + P\{i)y' + Po(')y = 0 is studied, where />,(/) are continuous real-valued and periodic of period 0. Various criteria are obtained which guarantee "partial" asymptotic stability or instability by means of effective bounds on the Floquet characteristic multipliers of Ly = 0.

Periodic Solutions for Third-order Nonlinear Delay Differential Equations with Variable Coefficients

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + d dt g (t, x (t− τ (t))) , is considered. By employing Green’s function, Krasnoselskii’s fixed point theorem and the contraction mapping principle, we state and prove the existence and uniqueness of periodic solutions...

Conditional Oscillation of Half-linear Differential Equations with Periodic Coefficients

We show that the half-linear differential equation (∗) [ r(t)Φ(x′) ]′ + s(t) tp Φ(x) = 0 with α-periodic positive functions r, s is conditionally oscillatory, i.e., there exists a constant K > 0 such that (∗) with γs(t) tp instead of s(t) tp is oscillatory for γ > K and nonoscillatory for γ < K.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Oscillation of Higher-order Linear Differential Equations with Entire Coefficients

This article is devoted to studying the solutions to the differential equation f (k) +Ak−1(z)f (k−1) + · · ·+A0(z)f = 0, k ≥ 2, where coefficients Aj(z) are entire functions of integer order. We obtain estimates on the orders and the hyper orders of the solutions to the above equation.