共查询到20条相似文献,搜索用时 15 毫秒
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This paper gives one-term componentwise asymptotics for theM and spectral matrices of a self-adjoint realisation of aneven-order ordinary differential expression. The underlyinginterval is assumed to have at least one regular endpoint, andthe boundary conditions are supposed to be separated. Furthermore,the weight function and the reciprocal of the highest-ordercoefficient are supposed to be of regular variation at the regularendpoint, in the sense of Bingham, Goldie and Teugels. 1991Mathematics Subject Classification: 34B24, 34E05. 相似文献
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Hani I. Siyyam 《Journal of Computational Analysis and Applications》2001,3(2):173-182
In this paper, we present two numerical methods for solving higher-order differential equations using the Laguerre Tau method. These methods generate linear systems, which can be solved by Gauss elimination with maximal partial pivoting strategy. Results of some numerical experiments and theoretical analysis are presented. 相似文献
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This paper examines global optimization of an integral objective function subject to nonlinear ordinary differential equations.
Theory is developed for deriving a convex relaxation for an integral by utilizing the composition result defined by McCormick
(Mathematical Programming 10, 147–175, 1976) in conjunction with a technique for constructing convex and concave relaxations
for the solution of a system of nonquasimonotone ordinary differential equations defined by Singer and Barton (SIAM Journal
on Scientific Computing, Submitted). A fully automated implementation of the theory is briefly discussed, and several literature
case study problems are examined illustrating the utility of the branch-and-bound algorithm based on these relaxations. 相似文献
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本文借助于Leibniz公式、复合函数的高阶导数公式以及变量替换的方法,给出了较为广泛的高阶非线性常微分方程的可积类型,有的还提供了通积分的表达式.所得结论推广了文献中的结果.最后列举了实例. 相似文献
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Manabu Naito 《Monatshefte für Mathematik》2002,117(1):237-242
This paper is concerned with the problem of counting the number of zeros of bounded nonoscillatory solutions of higher-order linear ordinary differential equations involving a parameter. It is shown that a recent result for the second-order case is still valid for the higher-order case. 相似文献
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Manabu Naito 《Monatshefte für Mathematik》2002,136(3):237-242
This paper is concerned with the problem of counting the number of zeros of bounded nonoscillatory solutions of higher-order
linear ordinary differential equations involving a parameter. It is shown that a recent result for the second-order case is
still valid for the higher-order case.
Received September 20, 2001; in revised form February 8, 2002 Published online July 12, 2002 相似文献
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本文论讨了三个问题:①二阶非线性微分方程的初值问题;②运用非线性算子证明了非平凡解的存在性和唯一性;③给出了一个非负非平凡解的估计式. 相似文献
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In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here. 相似文献
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Richard Haberman 《Studies in Applied Mathematics》1975,54(4):275-282
Nonlinear evolution equations are generated which correspond to isospectral differential-matrix eigenvalue problems. Although not discussed here, this procedure is appropriate for the analysis of the initial-value solution by the inverse-scattering method. In the 2 × 2 case the results obtained are consistent with other more general procedures. It yields the sine-Gordon equation, the reduced Maxwell-Bloch equations for self-induced transparency, and also a type of PBBM equation for long nonlinear water waves. In the n × n case, equations are derived corresponding to a new class of triad and multitriad resonant nonlinear interaction of wave envelopes. 相似文献
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非线性二阶常微分方程的正周期解 总被引:2,自引:0,他引:2
讨论一类非线性二阶常微分方程的周期解问题 ,利用Banach空间锥上的不动点定理得到了正周期解的存在性和多重性结果 ,大大改进了文献 [1 ]的结果 相似文献
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《复变函数与椭圆型方程》2012,57(2):143-154
In this article, existence and uniqueness of analytic solutions to a class of problems of the form $ zG^{\prime \prime }(z)+J(z)G^{\prime }(z)+F(G(z))=0, G(0)=G_0 $ are considered, where J is analytic in some neighborhood about 0 and F is analytic in some neighborhood of G 0 . This is a generalization of a class of problems considered by Rothe (F. Rothe (1997). A variant of Frobenius' method for the Emden-Fowler equation. Applicable Analysis , 66 , 227-245). 相似文献
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Yong Xiang LI 《数学学报(英文版)》2005,21(3):491-496
In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation -u″(t) = f(t, u(t)), where f : R^2 → R is a continuous odd function and is 2π-periodic in t. The discussion is based on the fixed point index theory in cones. 相似文献
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二阶非线性常微分方程的正周期解 总被引:29,自引:0,他引:29
本文应用Krasnoselskii锥映射不动点定理,研究了二阶非线性常微分方程的ω-周期解的存在性,获得了若干正ω-周期解的存在性与多重性结果. 相似文献