Nonlocal impulsive problems for nonlinear differential equations in Banach spaces

Mathematical and Computer Modelling

Volumn 49, Issue 3-4, 2009, Pages 798-804

  Liang, Jin ^a,b   Liu, James H ^c,d   Xiao, Ti Jun ^e  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c JAMES MADISON UNIVERSITY   (United States)

^d ANHUI UNIVERSITY   (China)

^e FUDAN UNIVERSITY   (China)

Author keywords

Nonlocal and impulsive conditions

Indexed keywords

BANACH SPACES; DIFFERENTIAL EQUATIONS; THEOREM PROVING; TOPOLOGY;

CLASSICAL SOLUTIONS; EXISTENCE AND UNIQUENESSES; IMPULSIVE DIFFERENTIAL EQUATIONS; NEW RESULTS; NONLINEAR DIFFERENTIAL EQUATIONS; NONLOCAL AND IMPULSIVE CONDITIONS; NONLOCAL CONDITIONS; STRONGLY CONTINUOUS SEMIGROUP;

NONLINEAR EQUATIONS;

EID: 58049145638     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2008.05.046     Document Type: Article

References (21)

1. Ahmed N.U. Optimal feedback control for impulsive systems on the space of finitely additive measures. Publ. Math. Debrecen 70 (2007) 371-393
2. Aizicovici S., and Lee H. Nonlinear nonlocal Cauchy problems in Banach spaces. Appl. Math. Lett. 18 (2005) 401-407
3. Byszewski L. Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162 (1991) 494-505
4. Byszewski L. Existence, uniqueness and asymptotic stability of solutions of abstract nonlocal Cauchy problems. Dynam. Systems Appl. 5 (1996) 595-605
5. Benchohra M., Henderson J., and Ntouyas S. Impulsive Differential Equations and Inclusions. Contemporary Mathematics and its Applications vol. 2 (2006), Hindawi Publ. Corp.
6. Byszewski L., and Lakshmikantham V. Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Applicable Anal. 40 (1990) 11-19
7. Boucherif A., and Precup R. On the nonlocal initial value problem for first order differential equations. Fixed Point Theory 4 2 (2003) 205-212
8. Ezzinbi K., Fu X., and Hilal K. Existence and regularity in the α-norm for some neutral partial differential equations with nonlocal conditions. Nonlinear Anal. 67 5 (2007) 1613-1622
9. Guo D., and Liu X. Extremal solutions of nonlinear impulsive integrodifferential equations in Banach spaces. J. Math. Anal. Appl. 177 (1993) 538-552
10. Henriquez H.R., Hernandez E., and Akca H. Global solutions for an abstract Cauchy problem with nonlocal conditions. Internat. J. Math. Manuscripts 1 (2007)
11. Jackson D. Existence and uniqueness of solutions of a semilinear nonlocal parabolic equations. J. Math. Anal. Appl. 172 (1993) 256-265
12. Liu J.H. Nonlinear impulsive evolution equations. Dynam. Contin. Discrete Impuls. Sys. 6 (1999) 77-85
13. Liang J., van Casteren J., and Xiao T.J. Nonlocal Cauchy problems for semilinear evolution equations. Nonlinear Anal. 50 (2002) 173-189
14. Lin Y., and Liu J.H. Semilinear integrodifferential equations with nonlocal Cauchy problem. Nonlinear Anal. 26 (1996) 1023-1033
15. Liang J., Liu J.H., and Xiao T.J. Nonlocal Cauchy problems governed by compact operator families. Nonlinear Anal. 57 (2004) 183-189
16. Liang J., and Xiao T.J. Semilinear integrodifferential equations with nonlocal initial conditions. Comput. Math. Appl. 47 (2004) 863-875
17. Liu X., and Willms A. Stability analysis and applications to large scale impulsive systems: A new approach. Canad. Appl. Math. Quart. 3 (1995) 419-444
18. Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems (1995), Birkhäuser Verlag, Basel
19. N'Guérékata G.M. Existence and uniqueness of an integral solution to some Cauchy problem with nonlocal conditions. Differential & Difference Equations and Applications (2006), Hindawi Publ. Corp., New York 843-849
20. Rogovchenko Y. Impulsive evolution systems: Main results and new trends. Dynam. Contin. Discrete Impuls. Sys. 3 (1997) 57-88
21. Zavalishchin A. Impulse dynamic systems and applications to mathematical economics. Dynam. Systems Appl. 3 (1994) 443-449