共查询到20条相似文献,搜索用时 15 毫秒
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This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients
of the forms
where τ, δ and σ are nonnegative integers and {p
n
}, {q
n
} and {c
n
} are nonnegative real sequences. Sufficient conditions for oscillation of the equations are obtained.
Research of the first author was supported by Department of Science and Technology, New Delhi, Govt. of India, under BOYSCAST
Programme vide Sanc. No. 100/IFD/5071/2004-2005 Dated 04.01.2005. 相似文献
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Sufficient conditions have been obtained for the existence of at least two non-negative periodic solutions to a system of first-order nonlinear functional differential equations. Applications to some ecological models are given. 相似文献
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Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived. 相似文献
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Bifurcations and exact traveling wave solutions of the equivalent complex short-pulse equations 下载免费PDF全文
In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrodinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions. 相似文献
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We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term Δu+|∇u|=p(|x|)f(u,v), Δv+|∇v|=q(|x|)g(u,v) on RN, N?3, provided that nonlinearities f and g are positive and continuous, the potentials p and q are continuous, c-positive and satisfy appropriate growth conditions at infinity. We find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity, while if f and g satisfy some growth conditions at infinity, and p, q are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded. 相似文献
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利用拓扑度理论及不动点指数理论,讨论了渐近线性算子方程的四种类型的解(即零解、正解、负解和变号解)的存在性,并将这一抽象结果应用于微分方程两点边值问题. 相似文献
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Vasile Dragan 《Journal of Difference Equations and Applications》2013,19(4):291-320
In this paper, a class of discrete-time backward non-linear equations defined on some ordered Hilbert spaces of symmetric matrices is considered. The problem of the existence of some global solutions is investigated. The class of considered discrete-time non-linear equations contains, as special cases, a great number of difference Riccati equations both from the deterministic and the stochastic framework. The results proved in the paper provide the sets of necessary and sufficient conditions that guarantee the existence of some special solutions of the considered equations as: the maximal solution, the stabilizing solution and the minimal positive semi-definite solution. These conditions are expressed in terms of the feasibility of some suitable systems of linear matrix inequalities (LMI). One shows that in the case of the equations with periodic coefficients to verify the conditions that guarantee the existence of the maximal or the stabilizing solution, we have to check the solvability of some systems of LMI with a finite number of inequations. The proofs are based on some suitable properties of discrete-time linear equations defined by the positive operators on some ordered Hilbert spaces chosen adequately. The results derived in this paper provide useful conditions that guarantee the existence of the maximal solution or the stabilizing solution for different classes of difference matrix Riccati equations involved in many problems of robust control both in the deterministic and the stochastic framework. The proofs are deterministic and are accessible to the readers less familiarized with the stochastic reasonings. 相似文献
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Wenting Liang 《Linear and Multilinear Algebra》2019,67(8):1606-1624
In this paper, we study the solvability of the operator equations in the general setting of infinite-dimensional Hilbert space with corresponding operators no necessarily having closed range. We get the necessary and sufficient conditions for the existences of the solutions and obtain formulae in each case for the general selfadjoint, positive and real positive solutions to these operator systems. 相似文献
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51.IntroductionInthispaper,westudythefollowingperiodicboundaryproblemwithNeumannboundaryconditionwhereO=RNisabounddomainwithC1 '(6>o)boundary.LetSuppose'm(x,t)eFandf.,.,$)eFforthe$beIongtoaboundsubsetofR,anditissat-isfiesForthesystem(1.1)',wesupposeitsati… 相似文献
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r-循环线性系统求解的快速算法 总被引:6,自引:0,他引:6
本文给出r-循环线性系统求解的一种快速算法.当r-循环矩阵非奇异时,该快速算法求出该线性系统的唯一解;当r-循环矩阵奇异时,该快速算法求出该线性系统的通解. 相似文献
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A. Tiryaki Department of Mathematics Gazi University Faculty of Arts Sciences Teknik Okullar Ankara Turkey S. 《数学物理学报(B辑英文版)》2001,21(2):182-188
1 IntroductionIn this paper we deal with the oscilIatory behaviour of solutions of nonlinear third orderdifferential equations of tlie formandwhere pt q E C([a,co),R) la E R, f E C(R,R) such that ap 3 g > 0 for V / 0 and 7 > 0 isa quotient of odd integers.By a proper solutiOn of (1) or (2) we mean a solution y of the equation which exi8ts on somehalf line [Tg, oo) 5 [a, oo), where Tv depens on y, and is llontirivial in some neighbourhood ofinfinity that is y(t) / 0 in [t., oo) fOr some t… 相似文献
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N. Parhi P. Das 《数学物理学报(B辑英文版)》1998,(1)
1IntroductionInthispaperwedealwithoscillatoryandnonoscillatorybehaviourofsolutionsofnonlinearthirdorderdifferentialequationsoftheformwherea,b,cEC([er,co),R),rrER,fEC(R,R)suchthatac2P>0fory/0and7>0isaquotientofoddintegers.From"Theoryofequations"tsee[1],itfollowsthattheequationwithconstantcoefficientsMoreover,allnonoscillatorysolutionsof(1.3)tendtozeroifandonlyifequatioll(l.3)hasanoscillatorysolution.Theseobservationsarefoundtobetruetoalargeextentformoregeneralequationsoftheformwherealb,cE… 相似文献
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An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB=C 总被引:1,自引:0,他引:1
An iteration method is constructed to solve the linear matrix equation AXB=C over symmetric X. By this iteration method, the solvability of the equation AXB=C over symmetric X can be determined automatically, when the equation AXB=C is consistent over symmetric X, its solution can be obtained within finite iteration steps, and its least-norm symmetric solution can be obtained by choosing a special kind of initial iteration matrix, furthermore, its optimal approximation solution to a given matrix can be derived by finding the least-norm symmetric solution of a new matrix equation
. Finally, numerical examples are given for finding the symmetric solution and the optimal approximation symmetric solution of the matrix equation AXB=C. 相似文献
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给出了矩阵方程AXB=D相容的又一充要条件,同时讨论它的极小范数解、最小二乘解和极小范数最小二乘解,推广了文献[1]和[3]的结论. 相似文献