AN OSCILLATION THEOREM FOR A TWO-PARAMETER SYSTEM OF DIFFERENTIAL EQUATIONS

Abstract

The oscillation theorem for two simultaneous Sturm-Liouville systems in two parameters is well known when the coefficients of the differential equations are subjected to the usual definiteness condition. However, in practical applications the usual definiteness condition may fail to hold, and hence in this paper we consider the oscillation theorem under another important definiteness condition.     

二阶常微分方程组积分边值问题的正解

在借助于非负矩阵获得正解的先验估计的基础上,用不动点指数理论研究二阶非线性常微分方程组积分边值问题正解和多重正解的存在性.     

A COMPARISON THEOREM FOR THE OSCILLATION OF DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENT

ＡＣＯＭＰＡＲＩＳＯＮＴＨＥＯＲＥＭＦＯＲＴＨＥＯＳＣＩＬＬＡＴＩＯＮＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＡＤＶＡＮＣＥＤＡＲＧＵＭＥＮＴＬｉＹｏｎｇｋｕｎ（李永昆）（ＹｕｎｎａｎＵｎｉｖｅｒｓｉｔｙ，云南大学，邮编：６５００９１）...     

AN OSCILLATION CRITERION FOR SECOND ORDER SUBLINEAR DIFFERENTIAL EQUATIONS

ＡＮＯＳＣＩＬＬＡＴＩＯＮＣＲＩＴＥＲＩＯＮＦＯＲＳＥＣＯＮＤＯＲＤＥＲＳＵＢＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＬｉＷａｎｔｏｎｇ（ＺｈａｎｇｙｅＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，７３４０００）ＱｕａｎＨｏｎｇｓｈｕｎ（Ｌａｎｚ...     

CONDITIONS FOR OSCILLATION OF NEUTRAL DELAY DIFFERENTIAL EQUATIONS

In this paper,we study one type of odd-order neutral delay differential equation. Suffcient conditions for the oscillation of every solution to this type of differential equation are given.     

EXPANSIONS IN EIGENFUNCTIONS OF A TWO-PARAMETER SYSTEM OF DIFFERENTIAL EQUATIONS. II

Abstract

In an earlier work we investigated the uniform convergence of the eigenfunction expansion associated with a two-parameter system of ordinary differential equations of the second order under left definiteness and semi-definiteness assumptions. In this paper we fix our attention upon the indefinite case.     

A STUDY OF A FULLY COUPLED TWO-PARAMETER SYSTEM OF SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL INTEGRO-MULTIPOINT BOUNDARY CONDITIONS

In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.     

REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITHN EUMANN BOUNDARY CONDITIONS

Inroductlonu consider here a system     

OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇｚｈｏｎｇ（靳明忠）（ＷｕｈａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｓｏｍ...     

某类高阶周期线性微分方程解的性质

本文研究了一类高阶周期系数线性微分方程解的性质问题. 利用复分析的相关理论和方法, 获得了在一些假设条件下, 当方程的系数 As 起控制作用时, 方程 f(k) + Ak-2f(k-2) + ...+Asf(s) + ... + A0f = 0 的任意两个线性无关解 f1,f2 满足λe(f1f2) ≥σe(As) 的结果, 推广了肖丽鹏的一个结果.     

二阶中立型微分方程振动比较定理

首先建立了一个Ｐｉｃｏｎｅ型的恒等式及两个Ｓｔｕｒｍ型的比较定理。利用它们定量地给出一类二阶中立型微分方程所有解振动的充分条件，著名的关于二阶常微分方程的Ｓｔｕｒｍ基本定理为本文定理之特例。     

ON THE TITCHMARSH-WEYL THEORY OF ORDINARY SYMMETRIC ODD-ORDER DIFFERENTIAL EXPRESSIONS AND A DIRECT CONVERGENCE THEOREM

Abstract

In this paper the odd-order differential equation M[y] λ wy on the interval (O,∞), associated with the symmetric differential expression M of (2k-1)st order (k ≥ 2) with w a positive weight function and λ a complex number, is shown to possess k-Titchmarsh-Weyl solutions for every non-real λ in the underlying Hilbert space L² _w(O, ∞) having identical representation for every non-real λ. In terms of these solutions the Green's function associated with the singular boundary value problem is shown to possess identical representation for all non-real λ which has been further made use of in the third-order case to establish a direct convergence eigenfunction expansion theorem. The symmetric spectral matrix appearing in the expansion theorem has been characterized in terms of the Titchmarsh-Weyl m-coefficients.     

A FOURIER-CHEBYSHEV SPECTRAL METHOD FOR THREE-DIMENSIONAL VORTICITY EQUATIONS WITH UNILATERAL PERIODIC BOUNDARY CONDITIONS

A mixed Fourier-Chebyshev spectral method is constructed for three-dimensional vorticity equations with unilateral periodic boundary condition. The generalized stability and the convergence are analyzed. The optimal error estimation is given. The technique in this paper is also suitable for other nonlinear problems.     

THE PERIODIC BOUNDARY PROBLE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH VARIABLE TIME

1 IntroductionIt is well known that the monotonic iterative technique is a successfulmethod to obtain the extremal solutions of ODE or IDE with fixed time (see[IJ, [2]). Some results about the monotonic iterative technique for IDE withvariable time were obtained in the past few years (see [3--7]). Because thetheory of IDE with variable time is more complicated than that of IDE withfixed time, many authors considered the special case in which the pulse surfacet = T(x) is strictly monoton…     

泛函微分方程周期边值问题的正解

讨论一阶泛函微分方程的周期边值问题,利用锥上的不动点定理给出了正解的存在性和多重性的简捷的判别条件.     

泛函微分方程周期边值问题的正解

讨论一阶泛函微分方程的周期边值问题,利用锥上的不动点定理给出了正解的存在性和多重性的简捷的判别条件.     

OSCILLATION FOR A CLASS OF SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH IMPULSES

This paper discusses the oscillation of second-order nonlinear differential equations with impulses.Sufficient conditions for all solutions of the equation to be oscillated are obtained.     

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATION OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

1 IntroductionRecently there wele a lot of activity concerning the oscillatory behavior ofsolutions of delay differential equations. We refer to the monographs [1,2,3,4].In particular, the oscillations and nonoscillations of solutions of the first orderneutral linear differential equation[x(t) -- p(t)x(t -- T)]' Q(t)x(t -- a) = 0 (*)have been investigated by many authors.In this paper, we consider the following first order nonlinear neutral diffe-rential equationwhereT) a E (0, co), al(t) …     

带有积分边界条件的非线性四阶奇异微分方程组的正解

通过构造一个特殊的锥,并在锥上应用不动点定理,得到了具有积分边界条件的四阶奇异微分方程组单个正解、多个正解的存在性和方程组正解的不存在性.     

带有边界值问题的脉冲分数阶微分方程正解的存在性

本文研究了具有边界值条件的脉冲分数阶微分方程.利用Kuratowski非紧性测度理论和Sadovskii不动点定理,得到了脉冲分数阶微分方程正解的存在性的结果,推广了已有文献的结论.