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1.
The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses Our results, which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations, improve and generalize the known results recently obtained in [8]. Received September 7, 1997, Revised May 26, 1998, Accepted July 15, 1998  相似文献
2.
In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear stochastic integro-differential evolution equations associated with abstract Volterra equations. Some examples are also given to illustrate our theory.  相似文献
3.
In this paper, we deal with Lp(p > 1) solutions to one dimensional backward stochastic differential equations(BSDEs) with discontinuous(left or right continuous)generators. We obtain an existence theorem of Lpsolutions to BSDEs whose generators are discontinuous, monotonic in y and uniformly continuous in z.  相似文献
4.
In this paper we study a stochastic Volterra-Levin equation. By using fixed point theory, we give some conditions for ensuring that this equation is exponentially stable in mean square and is also almost surely exponentially stable. Our result generalizes and improves on the results in [14], [1] and [30].  相似文献
5.
In this paper, we study the existence and uniqueness of the solution to a class of doubly perturbed jump-diffusion processes with non-Lipschitz coefficients. Some well-known results are improved and generalized.  相似文献
6.
In this paper, we consider a class of stochastic neutral partial functional differential equations in a real separable Hilbert space. Some conditions on the existence and uniqueness of a mild solution of this class of equations and also the exponential stability of the moments of a mild solution as well as its sample paths are obtained. The known results in Govindan [T.E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77 (2005) 139-154], Liu and Truman [K. Liu, A. Truman, A note on almost sure exponential stability for stochastic partial functional differential equations, Statist. Probab. Lett. 50 (2000) 273-278] and Taniguchi [T. Taniguchi, Almost sure exponential stability for stochastic partial functional differential equations, Stoch. Anal. Appl. 16 (1998) 965-975; T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics 53 (1995) 41-52] are generalized and improved.  相似文献
7.
The fixed-point theory is first used to consider the stability for stochastic partial differential equations with delays. Some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given. These conditions do not require the monotone decreasing behavior of the delays, which is necessary in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763; Ruhollan Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, Stoch. Anal. Appl. 21 (2003) 161-181]. Even in this special case, our results also improve the results in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763].  相似文献
8.
A strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. The Razumikhin–Lyapunov type function methods and comparison principles are studied in pursuit of sufficient conditions for the moment exponential stability and almost sure exponential stability of equations in which we are interested. The results of [A.V. Svishchuk, Yu.I. Kazmerchuk, Stability of stochastic delay equations of Itô form with jumps and Markovian switchings, and their applications in finance, Theor. Probab. Math. Statist. 64 (2002) 167–178] are generalized and improved as a special case of our theory.  相似文献
9.
In this paper we consider a nonlinear scalar delay differential equation with variable delays and give some new conditions for the boundedness and stability by means of Krasnoselskii’s fixed point theory. A stability theorem with a necessary and sufficient condition is proved. The results in [T.A. Burton, Stability by fixed point theory or Liapunov’s theory: A comparison, Fixed Point Theory 4 (2003) 15–32; T.A. Burton, T. Furumochi, Asymptotic behavior of solutions of functional differential equations by fixed point theorems, Dynamic Systems and Applications 11 (2002) 499–519; B. Zhang, Fixed points and stability in differential equations with variable delays, Nonlinear Analysis 63 (2005) e233–e242] are improved and generalized. Some examples are given to illustrate our theory.  相似文献
10.
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