A note on the existence and uniqueness of mild solutions to neutral stochastic partial functional differential equations with non-Lipschitz coefficients

被引：34

作者：

Jiang, Feng

Shen, Yi ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 61卷 / 06期

基金：

美国国家科学基金会;

关键词：

Caratheodory condition; Non-Lipschitz condition; Mild solution; Neutral stochastic partial functional differential equations; SUCCESSIVE-APPROXIMATIONS;

D O I：

10.1016/j.camwa.2011.01.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we study the existence and uniqueness of mild solutions to neutral stochastic partial functional differential equations under some Caratheodory-type conditions on the coefficients by means of the successive approximation. In particular, we generalize and improve the results that appeared in Govindan [T.E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77 (2005) 139-154] and Bao and Hou [J. Bao, Z. Hou, Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients, Comput. Math. Appl. 59 (2010) 207-214]. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1590 / 1594

页数：5

共 50 条

[1] Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients
Bao, Jianhai
Hou, Zhenting
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (01) : 207 - 214
[2] Mild solution of neutral stochastic partial functional integrodifferential equations with non-Lipschitz coefficients
Diop M.A.
Ezzinbi K.
Lo M.
[J]. Afrika Matematika, 2013, 24 (4) : 671 - 682
[3] ON THE PATHWISE UNIQUENESS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS
Zhang, Defei
He, Ping
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2013, 43 (05) : 1739 - 1746
[4] Existence and uniqueness of solutions to stochastic Volterra equations with singular kernels and non-Lipschitz coefficients
Wang, Zhidong
[J]. STATISTICS & PROBABILITY LETTERS, 2008, 78 (09) : 1062 - 1071
[5] INVARIANT MEASURE FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS
Stanzhytsky, Andriy
Misiats, Oleksandr
Stanzhytskyi, Oleksandr
[J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2022, 11 (06): : 1929 - 1953
[6] EXISTENCE AND UNIQUENESS OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ DIFFUSION AND POISSON MEASURE
Zubchenko, V. P.
Mishura, Yu. S.
[J]. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2009, 80 : 43 - 54
[7] Continuity and approximation properties of solutions to fractional neutral stochastic functional differential equations with non-Lipschitz coefficients
Wen, Jiaping
He, Ping
Lv, Wujun
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2023, 95 (04) : 662 - 695
[8] Averaging principle for neutral stochastic functional differential equations with impulses and non-Lipschitz coefficients
Cui, Jing
Bi, Nana
[J]. STATISTICS & PROBABILITY LETTERS, 2020, 163
[9] Existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay under non-Lipschitz conditions
Fengying Wei
Yuhua Cai
[J]. Advances in Difference Equations, 2013
[10] Existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay under non-Lipschitz conditions
Wei, Fengying
Cai, Yuhua
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2013,

← 1 2 3 4 5 →