Sharp Oscillation Criteria for Fourth Order Sub-half-linear and Super-half-linear Differential Equations
نویسندگان
چکیده
This paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation (E) (p(t)|x| x)′′ + q(t)|x|x = 0 , where α > 0, β > 0 are constants and p, q : [a,∞) → (0,∞) are continuous functions satisfying conditions
منابع مشابه
Forced oscillation of super-half-linear impulsive differential equations
By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملA Survey on Oscillation of Impulsive Ordinary Differential Equations
This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included.
متن کاملInterval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay
We study the following second-order super-half-linear impulsive differential equations with delay r t φγ x′ t ′ p t φγ x t − σ q t f x t − σ e t , t / τk, x t akx t , x′ t bkx′ t , t τk , where t ≥ t0 ∈ R, φ∗ u |u|∗−1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence with τ1 < τ2 < · · · < τk < · · · , limk→∞τk ∞, and τk 1 − τk > σ. By some classical inequalities, Ricca...
متن کاملDynamic Systems and Applications 24 (2015) 211-220 LYAPUNOV TYPE INEQUALITIES FOR SECOND ORDER SUB AND SUPER-HALF-LINEAR DIFFERENTIAL EQUATIONS
In the case of oscillatory potential, we present a Lyapunov type inequality for second order differential equations of the form (r(t)Φβ(x ′(t)))′ + q(t)Φγ(x(t)) = 0, in the sub-half-linear (0 < γ < β) and the super-half-linear (0 < β < γ < 2β) cases where Φ∗(s) = |s|∗−1s. AMS (MOS) Subject Classification. 34C10, 34C15.
متن کاملHalf-Linear Dynamic Equations
Abstract. We survey half-linear dynamic equations on time scales. These contain the well-known half-linear differential and half-linear difference equations as special cases, but also other kinds of half-linear equations. Special cases of half-linear equations are the well-studied linear equations of second order. We discuss existence and uniqueness of solutions of corresponding initial value p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008