Geodesic
Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Functional Differential Equations with Infinite Delays
Vinodkumar, A.1
1 Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore-641 004, Tamil Nadu, India
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 236-246.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This article presents the results on existence, uniqueness and stability of mild solution for impulsive stochastic semilinear functional differential equations with non-Lipschitz condition and Lipschitz condition. The results are obtained by using the method of successive approximation and Bihari’s inequality.
DOI : 10.22436/jnsa.004.04.02
Classification : 93E15, 60H15, 35R12
Keywords: Existence, Uniqueness, Stability, Successive approximation, Bihari’s inequality.

Vinodkumar, A. 1

1 Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore-641 004, Tamil Nadu, India 
@article{JNSA_2011_4_4_a1,
     author = {Vinodkumar, A.},
     title = {Existence, {Uniqueness} and {Stability} {Results} of {Impulsive} {Stochastic} {Semilinear} {Functional} {Differential}  {Equations} with {Infinite} {Delays}},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {236-246},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2011},
     doi = {10.22436/jnsa.004.04.02},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.02/}
}
TY  - JOUR
AU  - Vinodkumar, A.
TI  - Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Functional Differential  Equations with Infinite Delays
JO  - Journal of nonlinear sciences and its applications
PY  - 2011
SP  - 236
EP  - 246
VL  - 4
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.02/
DO  - 10.22436/jnsa.004.04.02
LA  - en
ID  - JNSA_2011_4_4_a1
ER  - 
%0 Journal Article
%A Vinodkumar, A.
%T Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Functional Differential  Equations with Infinite Delays
%J Journal of nonlinear sciences and its applications
%D 2011
%P 236-246
%V 4
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.02/
%R 10.22436/jnsa.004.04.02
%G en
%F JNSA_2011_4_4_a1
Vinodkumar, A. Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Functional Differential  Equations with Infinite Delays. Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 236-246. doi : 10.22436/jnsa.004.04.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.02/

[1] Anguraj, A.; Arjunan, M. M.; E. Hernández Existence results for an impulsive partial neutral functional differential equations with state - dependent delay, Appl. Anal. , Volume 86 (2007), pp. 861-872

[2] Anguraj, A.; A.Vinodkumar Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Neutral Functional Differential Equations with Infinite Delays, E .J. Qualitative Theory of Differential Equations , Volume 67 (2009), pp. 1-13

[3] Bao, J.; Z. Hou Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients, J. Comput. Math. Appl. , Volume 59 (2010), pp. 207-214

[4] I. Bihari A generalization of a lemma of Bellman and its application to uniqueness problem of differential equations, Acta Math. Acad. Sci. Hungar. , Volume 7 (1956), pp. 71-94

[5] Prato, G. Da; Zabczyk, J. Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992

[6] Govindan, T. E. Stability of mild solutions of stochastic evolution equations with variable delay, Stochastic Anal. Appl. , Volume 21 (2003), pp. 1059-1077

[7] Hernández, E.; Rabello, M.; Henriquez, H. R. Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Appl. , Volume 331 (2007), pp. 1135-1158

[8] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S. Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989

[9] Pazy, A. Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Newyork, 1983

[10] Ren, Y.; Xia, N. Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput. , Volume 210 (2009), pp. 72-79

[11] Ren, Y.; Lu, S.; Xia, N. Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math. , Volume 220 (2008), pp. 364-372

[12] Sakthivel, R.; J. Luo Asymptotic stability of impulsive stochastic partial differential equations with infinite delays, J. Math. Anal. Appl. , Volume 342 (2009), pp. 753-760

[13] Sakthivel, R.; Luo, J. Asymptotic stability of nonlinear impulsive stochastic differential equations , Statist. Probab. Lett. , Volume 79 (2009), pp. 1219-1223

[14] Samoilenko, A. M.; Perestyuk, N. A. Impulsive Differential Equations, World Scientific, Singapore, 1995

[15] Yang, J.; Zhong, S.; Luo, W. Mean square stability analysis of impulsive stochastic differential equations with delays, J. Comput. Appl. Math. , Volume 216 (2008), pp. 474-483

[16] Yang, Z.; Xu, D.; Xiang, L. Exponential p- stability of impulsive stochastic differential equations with delays, Physics Letter A , Volume 356 (2006), pp. 129-137

Cité par Sources :