کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4633475 | 1340671 | 2009 | 5 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay A note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay](/preview/png/4633475.png)
In this note, we prove the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay (INSFDEs in short) in which the initial value belongs to the phase space BC((-∞,0]Rd)BC((-∞,0]Rd), which denotes the family of bounded continuous RdRd-value functions φφ defined on (-∞,0](-∞,0] with norm ||φ||=sup-∞<θ⩽0|φ(θ)|||φ||=sup-∞<θ⩽0|φ(θ)|, under some Carathéodory-type conditions on the coefficients by means of the successive approximation. Especially, we extend the results appeared in Ren et al. [Y. Ren, S. Lu, N. Xia, Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math. 220 (2008) 364–372], Ren and Xia [Y. Ren, N. Xia, Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput. 210 (2009) 72–79] and Zhou and Xue [S. Zhou, M. Xue, The existence and uniqueness of the solutions for neutral stochastic functional differential equations with infinite delay, Math. Appl. 21 (2008) 75–83].
Journal: Applied Mathematics and Computation - Volume 214, Issue 2, 15 August 2009, Pages 457–461