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981.
A Note on the Oscillation of Second Order Differential Equations 总被引:1,自引:0,他引:1
We give a sufficient condition for the oscillation of linear homogeneous second order differential equation y + p(x)y + q(x)y = 0, where and is positive real number. 相似文献
982.
H.D Voulov 《Journal of Mathematical Analysis and Applications》2004,296(1):32-43
We prove that every positive solution of the third order difference equation
983.
Yihong Song Christopher T.H. Baker 《Journal of Mathematical Analysis and Applications》2004,294(1):310-333
Various different types of stability are defined, in a unified framework, for discrete Volterra equations of the type x(n)=f(n)+∑nj=0K(n,j,x(n)) (n?0). Under appropriate assumptions, stability results are obtainable from those valid in the linear case (K(n,j,x(n))=B(n,j)x(j)), and a linearized stability theory is studied here by using the fundamental and resolvent matrices. Several necessary and sufficient conditions for stability are obtained for solutions of the linear equation by considering the equations in various choices of Banach space , the elements of which are sequences of vectors (, , n,j?0, etc.). We show that the theory, including a number of new results as well as results already known, can be presented in a systematic framework, in which results parallel corresponding results for classical Volterra integral equations of the second kind. 相似文献
984.
G. Papaschinopoulos 《Journal of Mathematical Analysis and Applications》2004,289(1):216-230
In this paper we study the boundedness and the asymptotic behavior of the positive solutions of the system of difference equations
985.
When a positive integer is expressed as a sum of squares, with each successive summand as large as possible, the summands decrease rapidly in size until the very end, where one may find two 's, or several 's. We find that the set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way.
986.
Espen Robstad Jakobsen 《Proceedings of the American Mathematical Society》2004,132(11):3203-3213
In this paper we provide and analyze a nonlinear degenerate parabolic equation in one space dimension with the following smoothing property: If the initial data is only uniformly continuous, at positive times, the solution has bounded second derivatives (it belongs to ). We call this surprising phenomenon a regularizing effect. So far, such phenomena have only been observed in uniformly parabolic equations.
987.
Jun Zhao. 《Mathematics of Computation》2004,73(247):1089-1105
We provide an error analysis of finite element methods for solving time-dependent Maxwell problem using Nedelec and Thomas-Raviart elements. We study the regularity of the solution and develop some new error estimates of Nedelec finite elements. As a result, the optimal -error bound for the semidiscrete scheme is obtained.
988.
In this paper, we describe an approximation technique for div-curl systems based in where is a domain in . We formulate this problem as a general variational problem with different test and trial spaces. The analysis requires the verification of an appropriate inf-sup condition. This results in a very weak formulation where the solution space is and the data reside in various negative norm spaces. Subsequently, we consider finite element approximations based on this weak formulation. The main approach of this paper involves the development of ``stable pairs" of discrete test and trial spaces. With this approach, we enlarge the test space so that the discrete inf-sup condition holds and we use a negative-norm least-squares formulation to reduce to a uniquely solvable linear system. This leads to optimal order estimates for problems with minimal regularity which is important since it is possible to construct magnetostatic field problems whose solutions have low Sobolev regularity (e.g., with ). The resulting algebraic equations are symmetric, positive definite and well conditioned. A second approach using a smaller test space which adds terms to the form for stabilization will also be mentioned. Some numerical results are also presented.
989.
In this paper we study the rotational form of the pressure-correction method that was proposed by Timmermans, Minev, and Van De Vosse. We show that the rotational form of the algorithm provides better accuracy in terms of the -norm of the velocity and of the -norm of the pressure than the standard form.
990.
Bernard Dacorogna Paolo Marcellini 《Transactions of the American Mathematical Society》2004,356(11):4643-4653
Consider the differential inclusion in . We exhibit an explicit solution that we call fundamental. It also turns out to be a viscosity solution when properly defining this notion. Finally, we consider a Dirichlet problem associated to the differential inclusion and we give an iterative procedure for finding a solution.