共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we initiate the oscillation theory for $h$-fractional difference equations of the form
\begin{equation*}
\begin{cases}
_{a}\Delta^{\alpha}_{h}x(t)+r(t)x(t)=e(t)+f(t,x(t)),\ \ \ t\in\mathbb{T}_{h}^{a},\ \ 1<\alpha<2,\x(a)=c_{0},\ \ \Delta_{h}x(a)=c_{1},\ \ \ c_{0}, c_{1}\in\mathbb{R},
\end{cases}
\end{equation*}
where $_{a}\Delta^{\alpha}_{h}$ is the Riemann-Liouville $h$-fractional difference of order $\alpha,$ $\mathbb{T}_{h}^{a}:=\{a+kh, k\in\mathbb{Z^{+}}\cup\{0\}\},$ and $a\geqslant0,$ $h>0.$
We study the oscillation of $h$-fractional difference equations
with Riemann-Liouville derivative, and obtain some sufficient
conditions for oscillation of every solution. Finally, we give an
example to illustrate our main results. 相似文献
2.
Shengping Chen 《Journal of Applied Mathematics and Computing》2009,31(1-2):495-506
Some new oscillation theorems for even-order difference equations of the form $$\Delta(|\Delta^{k-1}x_{n}|^{\alpha-1}\Delta ^{k-1}x_{n})+f(n,x_{\sigma(n)})=0$$ are obtained. Our results generalize some well-known results for second order difference equations. 相似文献
3.
Oscillation of 2nd-order Nonlinear Noncanonical Difference Equations with Deviating Argument 下载免费PDF全文
The purpose of this paper is to establish some new criteria for the
oscillation of the second-order nonlinear noncanonical difference equations
of the form
\[
\Delta \left( a\left( n\right) \Delta x\left( n\right) \right) +q(n)x^{\beta
}\left( g(n)\right) =0,\text{ \ \ }n\geq n_{0}
\]
under the assumption
\[
\sum_{s=n}^{\infty }\frac{1}{a\left( s\right) }<\infty \text{.}
\]
Corresponding difference equations of both retarded and advanced type are
studied. A particular example of Euler type equation is provided in order to
illustrate the significance of our main results. 相似文献
4.
COMPARISON AND OSCILLATION THEOREMS FOR AN ADVANCED TYPE DIFFERENCE EQUATIONCOMPARISONANDOSCILLATIONTHEOREMSFORANADVANCEDTYPE... 相似文献
5.
6.
In this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation $$\left[ {r\left( t \right)\left[ {m\left( t \right)y\left( t \right) + p\left( t \right)y\left( {\tau \left( t \right)} \right)} \right]^\Delta } \right]^\Delta + q\left( t \right)f\left( {y\left( {\delta \left( t \right)} \right)} \right) = 0$$ on a time scale $\mathbb{T}$ which is unbounded above, where m, p, q, r, T and δ are real valued rd-continuous positive functions defined on $\mathbb{T}$ . The main investigation of the results depends on the Riccati substitutions and the analysis of the associated Riccati dynamic inequality. The results complement the oscillation results for neutral delay dynamic equations and improve some oscillation results for neutral delay differential and difference equations. Some examples illustrating our main results are given. 相似文献
7.
In this paper, we first consider difference equations with several delays in the neutral term of the form * $$\Delta\left(y_{n}+\sum_{i=1}^{L}p_{i}y_{n-{k_{i}}}-\sum_{j=1}^{M}r_{j}y_{n-{\rho_{j}}}\right)+q_{n}y_{n-\tau}=0\quad \mbox{for}\ n\in\mathbb{Z}^{+}(0),$$ study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution of (*) under some hypotheses. Moreover, we consider reaction-diffusion difference equations with several delays in the neutral term of the form $$\begin{array}{l}\Delta_{1}\left(u_{n,m}+\displaystyle \sum_{i=1}^{L}p_{i}u_{n-{k_{i}},m}-\displaystyle \sum_{j=1}^{M}r_{j}u_{n-{\rho_{j}},m}\right)+q_{n,m}u_{n-\tau,m}\\[18pt]\quad {}=a^{2}\Delta_{2}^{2}u_{n+1,m-1}\end{array}$$ for (n,m)∈?+(0)×Ω, study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution under some hypotheses. 相似文献
8.
In this paper, sufficient conditions have been obtained for oscillation of all solutions of a class of nonlinear neutral delay
difference equations of the form
$
\Delta \left( {r\left( n \right)\Delta \left( {y\left( n \right) + p\left( n \right)y\left( {n - m} \right)} \right)} \right) + q\left( n \right)G\left( {y\left( {n - k} \right)} \right) = 0
$
\Delta \left( {r\left( n \right)\Delta \left( {y\left( n \right) + p\left( n \right)y\left( {n - m} \right)} \right)} \right) + q\left( n \right)G\left( {y\left( {n - k} \right)} \right) = 0
相似文献
9.
We study general parabolic equations of the form \(u_t = \text{ div }\,\mathbf {A}(x,t, u,D u) +\text{ div }\,(|\mathbf {F}|^{p-2} \mathbf {F})+ f\) whose principal part depends on the solution itself. The vector field \(\mathbf {A}\) is assumed to have small mean oscillation in x, measurable in t, Lipschitz continuous in u, and its growth in Du is like the p-Laplace operator. We establish interior Calderón–Zygmund estimates for locally bounded weak solutions to the equations when \(p>2n/(n+2)\). This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto (Degenerate parabolic equations, Springer, New York, 1993) and the maximal function free approach by Acerbi and Mingione (Duke Math J 136(2):285–320, 2007). 相似文献
10.
超线性时滞微分方程解的振动性 总被引:4,自引:0,他引:4
研究一阶超线性时滞微分方程x′(t) p(t)[x(t—γ)]^α=0(α>1)解的振动性及非振动性,获得了保证其所有解振动的“almost sharp”准则,并应用所得结果于混合型时滞微分方程x′(t) ∑^ni=1pi(t)[x(t-γi]^αi=0,得到一族振动准则。 相似文献
11.
Jianfeng Zhang. 《Mathematics of Computation》2006,75(256):1755-1778
In this paper we study finite difference approximations for the following linear stationary convection-diffusion equations:
12.
We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping under quite general conditions. These results are extensions of the recent results developed by Sun [Y.G. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations. 相似文献
13.
Ravi P. Agarwal Said R. Grace Patricia J. Y. Wong 《Journal of Applied Mathematics and Computing》2010,32(1):189-203
Some new criteria for the oscillation of third order nonlinear difference equations $$\begin{array}{l}\Delta^{2}\bigl(\frac{1}{a(k)}(\Delta x(k))^{\alpha}\bigr)+q(k)f(x[g(k)])=0\quad\mbox{and}\\[6pt]\Delta^{2}\bigl(\frac{1}{a(k)}(\Delta x(k))^{\alpha}\bigr)=q(k)f(x[g(k)])+p(k)h(x[\sigma(k)])\end{array}$$ are established. 相似文献
14.
S. R. Grace 《Czechoslovak Mathematical Journal》2000,50(2):347-358
15.
In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation 相似文献
$${\left( {r\left( t \right)g\left( {{x^\Delta }\left( t \right)} \right)} \right)^\Delta } + p\left( t \right)f\left( {x\left( {\tau \left( t \right)} \right)} \right) = 0,$$ 16.
This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients
of the forms
17.
Oscillation criteria for all solutions of the first order delay difference equation of the form
where {pn} is a sequence of nonnegative real numbers and k is a positive integer are established especially in the case that the well-known oscillation conditions
are not satisfied.
Dedicated to Professor Y.G. Sficas on the occasion of his 60h birthday 相似文献
18.
The paper is concerned with oscillation properties of n-th order neutral differential equations of the form
19.
Zhi-ting Xu 《应用数学学报(英文版)》2009,25(2):291-304
Using general means, we establish several new Philos-type oscillation theorems for the second order damped elliptic differential equation
Σi,j=1 N Di[aij(x)Djy]+Σi=1 N bi(x)Diy+c(x)f(y)=0 under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of Xu, Jia and Ma. 相似文献 20.
We investigate the unique solvability of second order parabolic equations in non-divergence form in , p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition,
they are VMO (vanishing mean oscillation) with respect to the remaining variables.
The second author was partially supported by NSF Grant DMS-0140405. 相似文献
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