共查询到20条相似文献,搜索用时 0 毫秒
1.
Optimal in a certain sense sufficient conditions are given for the existence and uniqueness of ω-periodic solutions of the
nonautonomous ordinary differential equation u
(2m)
=f(t,u,...,u
(m-1)
), where the function f:ℝ×ℝ
m
→ℝ is periodic with respect to the first argument with period ω.
Received: December 21, 1999; in final form: August 12, 2000?Published online: October 2, 2001 相似文献
2.
Zhiting Xu 《Monatshefte für Mathematik》2009,156(2):187-199
Some necessary and sufficient conditions for nonoscillation are established for the second order nonlinear differential equation
where p > 0 is a constant. These results are extensions of the earlier results of Hille, Wintner, Opial, Yan for second order linear
differential equations and include the recent results of Li and Yeh, Kusano and Yoshida, Yang and Lo for half-linear differential
equations.
Authors’ address: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China 相似文献
3.
The delay differential equation with piecewise constant argument x′(t)+a(t)x(t)+b(t)x([t-k])=0 is considered,where a(t) and b(t) are continuous functions on [-k,∞),b(t)≥0,k is a positive integer and [·] denotes the greatest integer function.Some new oscillation and nonoscillation conditions are obtained. 相似文献
4.
Zhiting Xu 《Monatshefte für Mathematik》2007,150(2):157-171
Some oscillation criteria are established by the averaging technique for the second order neutral delay differential equation
of Emden-Fowler type
where x(t) = y(t) + p(t)y(t − τ), τ, σ1 and σ2 are nonnegative constants, α > 0, β > 0, and a, p, q
1,
. The results of this paper extend and improve some known results. In particular, two interesting examples that point out
the importance of our theorems are also included. 相似文献
5.
Mourad E. H. Ismail 《Aequationes Mathematicae》1978,17(1):148-153
We show how to solve certain types of linear ordinary differential equations with variable coefficients by using Appell polynomials. 相似文献
6.
Bao Qin Li 《Archiv der Mathematik》2008,91(4):344-353
We describe meromorphic solutions of certain non-linear (ordinary and partial) differential equations in complex domains.
Received: 13 November 2007 相似文献
7.
Hernán R. Henríquez 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(5):797-822
We establish existence of asymptotically almost periodic mild solutions for a class of semi-linear second-order abstract retarded
functional differential equations with infinite delay.
Research supported in part by FONDECYT, grant 1050314. 相似文献
8.
The aim of this paper is to study a particular aspect of the stability of Meissner’s equation, which leads to some interesting questions about the invariance of the trace of a product of matrices. Received: March 3, 2000?Published online: July 13, 2001 相似文献
9.
S. M. Verduyn Lunel 《Integral Equations and Operator Theory》1995,22(1):93-122
In this paper we prove convergence results for the series expansion of the solution to a linear functional differential equation. The results are consequences of an analysis of eigenfunction expansions for the generator of the solution map. This abstract approach unifies the treatment of retarded and neutral functional differential equations.The research of S.M. Verduyn Lunel has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences 相似文献
10.
11.
In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on
a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples
of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
Received: 6 July 1999 / Revised version: 19 April 2000 /?Published online: 14 June 2001 相似文献
12.
13.
Olivier Guibé 《Annali di Matematica Pura ed Applicata》2002,180(4):441-449
We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem -div(a(x,Du))=μ in Ω, u=0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω.
Received: December 27, 2000 Published online: December 19, 2001 相似文献
14.
We consider the flow of a stochastic differential equation on d-dimensional Euclidean space. We show that if the Lie algebra generated by its diffusion vector fields is finite dimensional and solvable, then the flow is conjugate to the flow of a non-autonomous random differential equation, i.e. one can be transformed into the other via a random diffeomorphism of d-dimensional Euclidean space. Viewing a stochastic differential equation in this form which appears closer to the setting of ergodic theory, can be an advantage when dealing with asymptotic properties of the system. To illustrate this, we give sufficient criteria for the existence of global random attractors in terms of the random differential equation, which are applied in the case of the Duffing-van der Pol oscillator with two independent sources of noise. Received: 25 May 1999 / Revised version: 19 October 2000 / Published online: 26 April 2001 相似文献
15.
It is proved that the even-order equationy
(2n)
+p(t)y=0 is (n,n) oscillatory at if
相似文献
16.
Summary. We study a numerical method for second-order differential equations in which high-frequency oscillations are generated by
a linear part. For example, semilinear wave equations are of this type. The numerical scheme is based on the requirement that
it solves linear problems with constant inhomogeneity exactly. We prove that the method admits second-order error bounds which
are independent of the product of the step size with the frequencies. Our analysis also provides new insight into the m
ollified impulse method of García-Archilla, Sanz-Serna, and Skeel. We include results of numerical experiments with the sine-Gordon
equation.
Received January 21, 1998 / Published online: June 29, 1999 相似文献
17.
Summary. Edge Sobolev spaces are proposed as a main new tool for the investigation of weakly hyperbolic equations. The well-posedness
of the linear and semilinear Cauchy problem in the class of these edge Sobolev spaces is proved. An application to the propagation
of singularities for solutions to the semilinear problem is considered.
Received: October 3, 2000 Published online: December 19, 2001 相似文献
18.
This paper studies, under some natural monotonicity conditions, the theory (existence and uniqueness, a priori estimate,
continuous dependence on a parameter) of forward–backward stochastic differential equations and their connection with quasilinear
parabolic partial differential equations. We use a purely probabilistic approach, and allow the forward equation to be degenerate.
Received: 12 May 1997 / Revised version: 10 January 1999 相似文献
19.
Quanxin Zhang 《Journal of Computational and Applied Mathematics》2011,235(5):1180-1188
By using the generalized Riccati transformation and the inequality technique, we establish a few new oscillation criterions for certain second-order half-linear delay dynamic equations with damping on a time scale. Our results extend and improve some known results, but also unify the oscillation of the second-order half-linear delay differential equation with damping and the second-order half-linear delay difference equation with damping. 相似文献
|