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1.
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
2.
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
3.
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
4.
51.IntroductionInthispaper,westudythefollowingperiodicboundaryproblemwithNeumannboundaryconditionwhereO=RNisabounddomainwithC1 '(6>o)boundary.LetSuppose'm(x,t)eFandf.,.,$)eFforthe$beIongtoaboundsubsetofR,anditissat-isfiesForthesystem(1.1)',wesupposeitsati… 相似文献
5.
6.
Bifurcations and exact traveling wave solutions of the equivalent complex short-pulse equations
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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
7.
8.
Oleg Palumbíny 《Czechoslovak Mathematical Journal》1999,49(4):779-790
The paper deals with the oscillation of a differential equation L
4
y + P(t)L
2
y + Q(t)y 0 as well as with the structure of its fundamental system of solutions. 相似文献
9.
本文在f(x,u)关于|u|的非常系数非线性控制下研究Hammerstein方程的可解性和解集的性状. 相似文献
10.
Symmetric positive solutions for second order boundary value problems with integral
boundary conditions on time scales
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This paper investigates the existence of symmetric positive
solutions for a class of nonlinear boundary value problem of second
order dynamic equations with integral boundary conditions on time
scales. Under suitable conditions, the existence of symmetric
positive solution is established by using monotone iterative
technique 相似文献
11.
12.
13.
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
14.
Ana I. Alonso Rafael Obaya Rafael Ortega 《Proceedings of the American Mathematical Society》2003,131(3):851-857
The present paper is concerned with scalar differential equations of first order which are limit periodic in the independent variable. Some tools provided by the theories of exponential dichotomies and periodic differential equations are applied to prove that, in a generic sense, the existence of a bounded solution implies the existence of a limit periodic solution.
15.
Xun-Hua Gong 《Journal of Mathematical Analysis and Applications》2008,342(2):1455-1466
In this paper, we present the necessary and sufficient conditions for weakly efficient solution, Henig efficient solution, globally efficient solution, and superefficient solution to the vector equilibrium problems with constraints. As applications, we give the necessary and sufficient conditions for corresponding solution to the vector variational inequalities and vector optimization problems. 相似文献
16.
Takashi Maeda 《Applied mathematics and computation》2010,217(3):1150-1157
In this paper, we consider constrained optimization problems with set-valued objective maps. First, we define three types of quasi orderings on the set of all non-empty subsets in n-dimensional Euclidean space and investigate their properties. Next, by using these orderings, we define the concepts of the convexities to set-valued maps and investigate their properties. Finally, based on these results, we define the concepts of optimal solutions to constrained optimization problems with set-valued objective maps and characterize their properties. 相似文献
17.
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
18.
Robert A. Van GorderK. Vajravelu 《Applied mathematics and computation》2011,217(12):5810-5821
We consider a convective flow in a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with suction, and internal heat generation/absorption. Using a similarity transformation the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations. We first examine a number of special cases for which we may obtain exact solutions. We then obtain analytical solutions (by the Homotopy Analysis Method) and numerical solutions (by a boundary value problem solver), in order to further study the behavior of the nonlinear differential equations, for various values of the physical parameters. Our numerical solutions are shown to agree with the available results in the literature. We then employ the numerical results to bring out the effects of the suction parameter, heat source/sink parameter, stretching parameter, porosity parameter, the Prandtl number and the free convection parameter on the flow and heat transfer characteristics. In the absence of suction and free convection, our findings are in agreement with the corresponding numerical results of Attia [H.A. Attia, On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation, Comput. Mater. Sci. 38 (2007) 741-745]. 相似文献
19.
Yongxin Yuan 《Applied mathematics and computation》2010,216(10):3120-3125
The least-squares solution and the least-squares symmetric solution with the minimum-norm of the matrix equations AX = B and XC = D are considered in this paper. By the matrix differentiation and the spectral decomposition of matrices, an explicit representation of such solution is given. 相似文献