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1.
Some new results are given concerning the behavior of the oscillatory solutions of first or second order delay differential equations. These results establish that all oscillatory solutions x of a first or second order delay differential equation satisfy x(t)=O(v(t)) as t→∞, where v is a nonoscillatory solution of a corresponding first or second order linear delay differential equation. Some applications of the results obtained are also presented. 相似文献
2.
Octavian G. Mustafa 《Journal of Mathematical Analysis and Applications》2008,348(1):211-219
We give a constructive proof of existence to oscillatory solutions for the differential equations x″(t)+a(t)λ|x(t)|sign[x(t)]=e(t), where t?t0?1 and λ>1, that decay to 0 when t→+∞ as O(t−μ) for μ>0 as close as desired to the “critical quantity” . For this class of equations, we have limt→+∞E(t)=0, where E(t)<0 and E″(t)=e(t) throughout [t0,+∞). We also establish that for any μ>μ? and any negative-valued E(t)=o(t−μ) as t→+∞ the differential equation has a negative-valued solution decaying to 0 at + ∞ as o(t−μ). In this way, we are not in the reach of any of the developments from the recent paper [C.H. Ou, J.S.W. Wong, Forced oscillation of nth-order functional differential equations, J. Math. Anal. Appl. 262 (2001) 722-732]. 相似文献
3.
By constructing a class of solutions to the integral inequality for t t0 large enough, where 0<A1a(τ)A2<+∞ and λ>1, that tend to zero as t→+∞ we address an open problem in the theory of nonlinear oscillations. 相似文献
4.
This paper is concerned with nonoscillatory solutions of the fourth order quasilinear differential equation
where α > 0, β > 0 and p(t) and q(t) are continuous functions on an infinite interval [a,∞) satisfying p(t) > 0 and q(t) > 0 (t≥a). The growth bounds near t = ∞ of nonoscillatory solutions are obtained, and necessary and sufficient integral conditions
are established for the existence of nonoscillatory solutions having specific asymptotic growths as t→∞.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Oleg Palumbíny 《Czechoslovak Mathematical Journal》1999,49(4):779-790
The paper deals with the oscillation of a differential equation L
4
y + P(t)L
2
y + Q(t)y 0 as well as with the structure of its fundamental system of solutions. 相似文献
6.
In this paper we consider positive unbounded solutions of second order quasilinear ordinary differential equations. Our objective
is to determine the asymptotic forms of unbounded solutions. An application to exterior Dirichlet problems is also given. 相似文献
7.
In this work, the asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses is investigated. By impulsive differential inequality and Riccati transformation, sufficient conditions of asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses are obtained. An example is also inserted to illustrate the impulsive effect. 相似文献
8.
9.
The asymptotic behavior of nonoscillatory solutions of the half-linear differential equation is studied. In particular, two Wronskian-type functions, which have some interesting properties, similar to the one of the Wronskian in the linear case, are given. Using these properties and suitable integral inequalities, the existence of the so-called intermediate solutions is examined and an open problem is solved. 相似文献
10.
Lihua Liu 《Journal of Computational and Applied Mathematics》2009,231(2):657-663
In this paper, several new oscillation criteria for the second-order nonlinear neutral delay differential equation
11.
本文讨论一类奇异拟线性椭圆型方程
-div(|x|-ap|▽u|p-2▽u)=μ+h(x)/|x|(a+1)p|u|p-2u+k(x)|u|p-2u/|x|bq,x∈RN,
其中1 < p < N, 0 ≤ a < N-p/p, a ≤ b < a + 1, 0 ≤ μ < μ = (N-p/p-a)p, q=p*(a, b) = Np/N-(1+a-b)p,h 和k 是RN上的连续有界函数, 且关于O(N) 的闭子群G满足某些对称性条件. 应用变分方法和Caffarelli-Kohn-Nirenberg 不等式, 在h与k满足适当条件下, 证得了一些G-对称解的存在性和多重性结果. 相似文献
12.
In this paper, the authors study the asymptotic behavior of solutions of second-order neutral type difference equations of the form
Δ2(yn+pyn−k)+f(n,yn−ℓ)=0,n