共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Bartušek M. Cecchi M. Marini 《Journal of Mathematical Analysis and Applications》2006,320(1):108-120
Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zero-counting function. 相似文献
2.
In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coeffiicient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented. 相似文献
3.
Approximate damped oscillatory solutions for compound KdV-Burgers equation and their error estimates
In this paper,we focus on studying approximate solutions of damped oscillatory solutions of the compound KdV-Burgers equation and their error estimates.We employ the theory of planar dynamical systems to study traveling wave solutions of the compound KdV-Burgers equation.We obtain some global phase portraits under different parameter conditions as well as the existence of bounded traveling wave solutions.Furthermore,we investigate the relations between the behavior of bounded traveling wave solutions and the dissipation coefficient r of the equation.We obtain two critical values of r,and find that a bounded traveling wave appears as a kink profile solitary wave if |r| is greater than or equal to some critical value,while it appears as a damped oscillatory wave if |r| is less than some critical value.By means of analysis and the undetermined coefficients method,we find that the compound KdV-Burgers equation only has three kinds of bell profile solitary wave solutions without dissipation.Based on the above discussions and according to the evolution relations of orbits in the global phase portraits,we obtain all approximate damped oscillatory solutions by using the undetermined coefficients method.Finally,using the homogenization principle,we establish the integral equations reflecting the relations between exact solutions and approximate solutions of damped oscillatory solutions.Moreover,we also give the error estimates for these approximate solutions. 相似文献
4.
George L. Karakostas S. Stević † 《Journal of Difference Equations and Applications》2013,19(9):809-815
The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation?in the title is investigated, where all the coefficients are nonnegative real numbers. The paper is motivated by an open problem proposed by Ladas [Open problems and conjectures, J. Differ. Equations?Appl., 5 (1999), 211–215]. 相似文献
5.
一类具正负系数中立型方程的正解 总被引:7,自引:1,他引:6
研究一类具有正负系数的中立型微分方程,得到了这类方程存在正解的充分条件和存在有界正解的充要条件,并据此给出了其存在无界正解的充分条件。 相似文献
6.
Joel E. Restrepo Durvudkhan Suragan 《Mathematical Methods in the Applied Sciences》2020,43(15):9080-9089
We give necessary conditions to get oscillatory solutions of a class of fractional order neutral differential equations with continuously distributed delay by means of the fractional derivative with respect to a given function. In particular, oscillatory solutions of the considered fractional equations with Caputo and Hadamard type of fractional derivatives are established. Some explicit examples are given to illustrate the main results. 相似文献
7.
一般Lidstone边值问题的n个正解的存在性 总被引:20,自引:2,他引:20
考察了含所有偶数阶导数的一般Lidstone边值问题的正解和对称正解.通过 选择合适的Banach空间和锥,对该问题建立了n个正解或者对称正解的存在性,其 中n是一个任意的自然数.基本工具是等价范数和锥拉伸与锥压缩型的Krasnosel'skii 不动点定理. 结论的主要条件是局部的.换言之,如果非线性项f在某些有界集上的 "高度"是适当的,则该问题可以具有n个正解. 相似文献
8.
9.
Symmetric positive solutions for second order boundary value problems with integral
boundary conditions on time scales
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This paper investigates the existence of symmetric positive
solutions for a class of nonlinear boundary value problem of second
order dynamic equations with integral boundary conditions on time
scales. Under suitable conditions, the existence of symmetric
positive solution is established by using monotone iterative
technique 相似文献
10.
研究了一类在无穷区间上具有p-Laplacian算子的边值问题的迭代正解.利用单调迭代方法得到问题的迭代正解存在性的充分条件,同时得到了解的相应迭代序列,最后给出例子证明所得结论. 相似文献
11.
本文考虑一类非线性延迟微分方程-带有单调造血率的造血模型数值解的振动性.通过研究特征方程根的情况得到数值解振动的条件并且讨论了非振动的数值解的一些性质.为了更有力的说明我们的结果,最后给出了相应的算例. 相似文献
12.
In this paper, by using the topological degree theory and the fixed point index theory, the existence of three kinds of solutions (i.e., sign-changing solutions, positive solutions and negative solutions) for asymptotically linear three-point boundary value problems is obtained. 相似文献
13.
This paper employs the theory of planar dynamical systems and undetermined coefficient method to study travelling wave solutions of the dissipative coupled Korteweg-de Vries equation. The possible kink profile solitary wave solutions and approximate damped oscillatory solutions of the equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. 相似文献
14.
具有正负系数中立型微分方程的正解 总被引:9,自引:0,他引:9
本文研究具有正负系数的中立型微分方程[X(t)-R(t)x(t-r)]'+P(t)x(t-r)-Q(t)x(t-δ)=0.在允许R(t)+Q(s)ds1不成立的条件下,获得方程(*)存在正解的两个充分条件. 相似文献
15.
研究了半线性高阶微分方程(m(t)[r(t)■p(y′(t))]~((n-1)))~((n))+q(t)■p(t))=f(t)的振动解的渐进性.利用H(o|¨)lder不等式给出了方程(1)的振动解渐进趋向于零的充分条件. 相似文献
16.
OscillationsofSecondOrderNonlinearNeutralDifferentialEquationsWandOiru;(王其如)WuYewei(武业伟)(LuogangTeachers'College,Luoyang47102... 相似文献
17.
OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY 总被引:1,自引:0,他引:1
冯月才 《Annals of Differential Equations》2004,20(1):37-40
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation. 相似文献
18.
The concept of unsaturated infinite double sequence is introduced by making use of frequency measures. Unsaturated solutions
are then studied for a partial difference equation. Conditions for all solutions to be unsaturated are obtained. Since unsaturated
solutions are oscillatory, our results yield oscillation criteria. 相似文献
19.
OSCILLATIONSOFFIRSTORDERNONLINEARRETARDEDDIFFERENTIALEQUATIONS¥WangQiru(王其如)(LuoyangTeachers'College,洛阳师范高等专科学校,邮编:471022)Abs... 相似文献
20.
孙喜东 《数学的实践与认识》2005,35(9):182-184
我们研究不稳定的二阶中立型差分方程解的振动问题Δ2[x(n)+px(n-τ)〗+q(n)x(g(n))=0,n>n0(1)建立了不稳定的二阶中立型差分方程(1)无界解的振动准则. 相似文献