Existence results for impulsive differential inclusions with nonlocal conditions

Computers and Mathematics with Applications

Volumn 62, Issue 4, 2011, Pages 1908-1915

  Ji, Shaochun ^a,b   Li, Gang ^b  

^a HUAIYIN INSTITUTE OF TECHNOLOGY   (China)

^b YANGZHOU UNIVERSITY   (China)

Author keywords

Fixed point theorems; Impulsive differential inclusions; Mild solutions; Multivalued analysis; Nonlocal conditions

Indexed keywords

DIFFERENTIAL INCLUSIONS; FIXED POINT THEOREMS; MILD SOLUTION; MULTIVALUED ANALYSIS; NON-LOCAL CONDITIONS;

DIFFERENTIAL EQUATIONS;

EID: 80051783598     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.06.034     Document Type: Article

References (32)

1. M. Benchohra, J. Henderson, and S.K. Ntouyas Impulsive Differential Equations and Inclusions vol. 2 2006 Hindawi Publishing Corporation New York
2. V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov Theory of Impulsive Differential Equations 1989 World Scientific Singapore
3. A.M. Samoilenko, and N.A. Perestyuk Impulsive Differential Equations 1995 World Scientific Singapore
4. N.U. Ahmed Measure solutions for impulsive evolution equations with measurable vector fields J. Math. Anal. Appl. 319 1 2006 74 93 (Pubitemid 43506847)
5. T. Cardinali, and P. Rubbioni Impulsive semilinear differential inclusion: topological structure of the solution set and solutions on non-compact domains Nonlinear Anal. 14 2008 73 84 (Pubitemid 351636406)
6. Y.K. Chang, A. Anguraj, and M. Mallika Arjunan Existence results for impulsive neutral functional differential equations with infinite delay Nonlinear Anal. 2 2008 209 218
7. C. Cuevas, E. Hernández, and M. Rabelo The existence of solutions for impulsive neutral functional differential equations Comput. Math. Appl. 58 2009 744 757
8. E. Hernández, M. Rabelo, and H.R. Henríquez Existence of solutions for impulsive partial neutral functional differential equations J. Math. Anal. Appl. 331 2007 1135 1158
9. S. Migorski, and A. Ochal Nonlinear impulsive evolution inclusion of second order Dynam. Systems Appl. 16 2007 155 174
10. S. Ji, and S. Wen Nonlocal Cauchy problem for impulsive differential equations in Banach spaces Int. J. Nonlinear Sci. 10 1 2010 88 95
11. S. Ji, G. Li, and M. Wang Controllability of impulsive differential systems with nonlocal conditions Appl. Math. Comput. 217 2011 6981 6989
12. L. Byszewski, and V. Lakshmikantham Theorem about the existence and uniqueness of solutions of a nonlocal Cauchy problem in a Banach space Appl. Anal. 40 1990 11 19
13. L. Byszewski Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem J. Math. Anal. Appl. 162 1991 494 505
14. S. Ntouyas, and P. Tsamotas Global existence for semilinear evolution equations with nonlocal conditions J. Math. Anal. Appl. 210 1997 679 687 (Pubitemid 127165334)
15. S. Ntouyas, and P. Tsamotas Global existence for semilinear integrodifferential equations with delay and nonlocal conditions Appl. Anal. 64 1997 99 105
16. J. Liang, J. Liu, and T. Xiao Nonlocal Cauchy problems governed by compact operator families Nonlinear Anal. 57 2004 183 189
17. S. Aizicovici, and M. McKibben Existence results for a class of abstract nonlocal Cauchy problems Nonlinear Anal. 39 2000 649 668 (Pubitemid 30515175)
18. S. Aizicovici, and H. Lee Nonlinear nonlocal Cauchy problems in Banach spaces Appl. Math. Lett. 18 2005 401 407 (Pubitemid 40302824)
19. M. Benchohra, J. Henderson, and S.K. Ntouyas Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces J. Math. Anal. Appl. 263 2001 763 780 (Pubitemid 33132696)
20. K. Ezzinbi, X. Fu, and K. Hilal Existence and regularity in the α-norm for some neutral partial differential equations with nonlocal conditions Nonlinear Anal. 67 2007 1613 1622 (Pubitemid 46634826)
21. J. García-Falset Existence results and asymptotic behavior for nonlocal abstract Cauchy problems J. Math. Anal. Appl. 338 2008 639 652
22. J. Liu A remark on the mild solutions of nonlocal evolution equations Semigroup Forum 66 2003 63 67 (Pubitemid 37503527)
23. X. Xue Nonlocal nonlinear differential equations with a measure of noncompactness in Banach spaces Nonlinear Anal. 70 2009 2593 2601
24. L. Zhu, and G. Li On a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general Banach spaces J. Math. Anal. Appl. 341 1 2008 660 675
25. J. Liang, J.H. Liu, and T.J. Xiao Nonlocal impulsive problems for nonlinear differential equations in Banach spaces Math. Comput. Modelling 49 2009 798 804
26. Z. Fan, and G. Li Existence results for semilinear differential equations with nonlocal and impulsive conditions J. Funct. Anal. 258 2010 1709 1727
27. H. Thiems Integrated semigroup and integral solutions to abstract Cauchy problem J. Math. Anal. Appl. 152 1990 416 447
28. R. Agarwal, M. Meehan, and D. O'Regan Fixed Point Theory and Applications Cambridge Tracts in Mathematics 2001 Cambridge University Press
29. A. Pazy Semigroups of Linear Operators and Applications to Partial Differential Equations 1983 Springer-Verlag New York
30. L. Zhu, and G. Li Nonlocal differential equations with multivalued perturbations in Banach spaces Nonlinear Anal. 69 2008 2843 2850
31. K. Deng Exponential decay of solutions of semilinear parabolic equations with non-local initial conditions J. Math. Anal. Appl. 179 1993 630 637
32. D. Jackson Existence and uniqueness of solutions of a semilinear nonlocal parabolic equations J. Math. Anal. Appl. 172 1993 256 265