共查询到20条相似文献,搜索用时 93 毫秒
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具有可变时滞的高阶非线性非自治差分方程的振动性 总被引:1,自引:0,他引:1
研究具有可变时滞的高阶非自治中立型差分方程Δm(xn-cnxn-k)+h(n,xn-ln)=0,n=0,1,2,…的振动性.利用方程的最终正解和最终负解导致序列{Δi(xn-cnxn-k)}(i=0,1,2,…,m-1)的最终单调和保号性,得到了这类差分方程振动的一系列充分条件. 相似文献
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具有可变时滞的非线性非自治差分方程的振动性及其应用 总被引:9,自引:0,他引:9
本文获得了一类具有可变时滞的非线性非自治差分方程的振动准则,建立了这类差分方程的几个线性化振动性定理,并得到了具有可变时滞的离散型非自治广义Logistic方程关于其正平衡点振动的一系列充分条件. 相似文献
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具强迫项高阶非线性中立型差分方程的振动性与渐近性 总被引:1,自引:1,他引:0
讨论具强迫项高阶非线性中立型差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=fn,n=0,1,2,…及其相关联的差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=0,n=0,1,2,…的振动性与渐近性,得到了所有解振动或趋于零的充分性判据. 相似文献
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研究了二阶中立型变时滞差分方程Δ2(xn+pxn-l)+qnf(xσ(n))=0解的振动性,获得了该类方程全部非平凡解振动的三个定理.所得结果将二阶中立型差分方程已有的振动性的相应结论推广到了二阶中立型变时滞差分方程. 相似文献
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杨甲山 《应用泛函分析学报》2014,(1):59-65
研究了一类具有最大值项和连续变量的非线性二阶中立型时滞差分方程的振动性,利用Banach空间的不动点原理和一些不等式技巧,得到了这类方程存在最终正解的充分条件,并得到了该方程振动的一些判别准则. 相似文献
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研究了一阶常系数中立型时滞差分方程A[x(n)-px(n-τ)]+qx(n-σ)=0的振动性.通过构造若干适当的函数,分别得到了在0
1两种情况下该方程的一切解振动的充分必要条件. 相似文献
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具连续变量的二阶非线性差分方程振动和非振动的充要条件 总被引:2,自引:0,他引:2
研究了一类具有连续变量的二阶非线性差分方程的振动性质,利用Banach空间的不动点原理和一些分析技巧,得到了这类方程存在非振动解的充分必要条件,并得到了这类方程振动的充分必要条件,同时给出了说明定理应用的例子. 相似文献
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利用Raccati变换技巧得到下列二阶非线性中立差分方程△(pn(△(sn+φ(n, Xτn))γ))+qnfβ(x9n)=0,n=0,1,2,...的一些振动性判别准则,这些结果改进了文献 [10,11]中的一些振动准则,并回答了一个公开问题,且改正了文献[10]中的一个定理及其证明. 相似文献
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Octavian G. Mustafa Yuri V. Rogovchenko 《Journal of Mathematical Analysis and Applications》2004,298(2):604-620
The paper is concerned with oscillation of a novel class of nonlinear differential equations with a damping term. First it is demonstrated how known oscillation results for another intensively studied class of equations can be translated to the one in question, and vice versa. Advantages and drawbacks of such translation are carefully examined. Then an oscillation criterion for the new class of equations is established. The principal result of the paper is compared to those reported in the literature, and an illustrative example to which known oscillation criteria fail to apply is provided. 相似文献
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一类非线性变系数差分方程正解的振动性 总被引:1,自引:0,他引:1
马满军 《纯粹数学与应用数学》2000,16(2):92-98
研究了一类具有时滞的非线笥变系数差分方程Xn+1=Xnexp(rn1-xn-k/1-cxn-k解的振动性,获得了其正解关于正平衡点x=1振动的好的充分条件。 相似文献
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In this paper, we first establish the equivalence of the oscillation of thedifference equations with several delays of the form: Δx_n+sum from i=1 to m(pi(n)x_(n-k_i))=0 for n≥0and the second-order difference equations without delay of the form:where{pj(n)}is a sequence of nonnegative real numbers and{k_i}_(i=1)~m is a setof positive integers. Then we get some "sharp" conditions for oscillation andnon-oscillation of the first equation. 相似文献
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OSCILLATION OF HIGHER ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS 总被引:1,自引:0,他引:1
OSCILLATIONOFHIGHERORDERNEUTRALDIFFERENTIALEQUATIONSWITHPOSITIVEANDNEGATIVECOEFFICIENTSLiWantong(李万同)(ZhangyeTeachers'College... 相似文献
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Zhenguo Zhang Xiaojing Lv Tian Yu 《Journal of Applied Mathematics and Computing》2003,13(1-2):125-138
Some Riccati type difference inequalities are established for the second-order nonlinear difference equations with negative neutral term $$\Delta (a(n)\Delta (x(n) - px(n - \tau ))) + f(n,x(\sigma (n))) = 0$$ using these inequalities we obtain some oscillation criteria for the above equation. 相似文献
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In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now. 相似文献
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An approximation theory is given for a class of elliptic quadratic forms which include the study of conjugate surfaces for elliptic multiple integral problems. These ideas follow from the quadratic form theory of Hestenes, applied to multiple integral problems by Dennemeyer, and extended with applications for approximation problems by Gregory.The application of this theory to a variety of approximation problem areas in this setting is given. These include conjugate surfaces and conjugate solutions in the calculus of variations, oscillation problems for elliptic partial differential equations, eigenvalue problems for compact operators, numerical approximation problems, and, finally, the intersection of these problem areas.In the final part of this paper the ideas are specifically applied to the construction and counting of negative vectors in order to obtain new numerical methods for solving Laplace-type equations and to obtain the “Euler-Lagrange equations” for symmetric-banded tridiagonal matrices. In this new result (which will allow the reexamination of both the theory and applications of symmetricbanded matrices) one can construct, in a meaningful way, negative vectors, oscillation vectors, eigenvectors, and extremal solutions of classical problems as well as efficient algorithms for the numerical solution of partial differential equations. Numerical examples (test runs) are given. 相似文献
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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