Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators

Numerical Functional Analysis and Optimization

Volumn 30, Issue 3-4, 2009, Pages 227-244

  Chang, Yong Kui ^a   Nieto, Juan J ^b  

^a NORTHWEST NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Analytic resolvent; Fixed point; Impulsive integro differential inclusions; Nonlocal initial condition

Indexed keywords

ANALYTIC RESOLVENT; DIFFERENTIAL INCLUSIONS; DIRICHLET; EXISTENCE OF SOLUTIONS; EXISTENCE THEOREM; FIRST-ORDER; FIXED POINT; FIXED POINT THEOREMS; FRACTIONAL OPERATORS; IMPULSIVE INTEGRO-DIFFERENTIAL INCLUSIONS; MILD SOLUTION; MULTIVALUED MAP; NONLOCAL INITIAL CONDITION; NONLOCAL INITIAL CONDITIONS; PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS; RESOLVENT OPERATORS; SUBLINEAR GROWTH;

INTEGRODIFFERENTIAL EQUATIONS;

MATHEMATICAL OPERATORS;

EID: 67651148207     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560902841146     Document Type: Article

References (28)

1. J. Banas and K. Goebel (1980). Measure of Noncompactness in Banach Spaces. Marcel Dekker, New York.
2. M. Benchohra and S. Ntouyas (2003). Existence and controllability results for multivalued semilinear differential equations with nonlocal conditions. Soochow J. Math. 29:157-170.
3. M. Benchohra, J. Henderson, and S. Ntouyas. (2006). Impulsive Differential Equations and Inclusions. Hindawi Publishing Corporation, New Hindawi Publishing Corporation, New York.
4. M. Benchohra, M. Hamami, and J.J. Nieto (in press). The method of upper and lower solutions for second order differential inclusions with integral boundary conditions. Rocky Mountain J. Math.
5. L. Byszewski (1991). Theorems about the existence and uniqueness of a solution of a semi-linear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162:496-505.
6. L. Byszewski (1998). Existence of solutions of semilinear functional-differential evolution nonlocal problem. Nonl. Anal. 34:65-72.
7. Y.-K. Chang and W.-T Li (2005). Existence results for second order impulsive functional differential inclusions. J. Math. Anal. Appl. 301:477-490.
8. Y.-K. Chang and W.-T. Li (2006). Existence results for impulsive dynamic equations on time scales with nonlocal initial conditions. Math. Comput. Modelling 43:377-384.
9. Y.-K. Chang, J.J. Nieto, and W.-S. Li (2009). On impulsive hyperbolic differential inclusions with nonlocal initial conditions. J. Optim. Theory Appl. 140:431-442.
10. B. Cui and M. Han (2008). Oscillation theorems for nonlinear hyperbolic systems with impulses. Nonlinear Anal. Real World Appl. 9:94-102.
11. K. Deimling (1992). Multivalued Differential Equations. de Gruyter, Berlin.
12. K. Ezzinbi and X. Fu (2004). Existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions. Nonlinear Anal. 57:1029-1041.
13. K. Ezzinbi, X. Fu, and K Hilal (2007). Existence and regularity in the α-norm for some neutral partial differential equations with nonlocal conditions. Nonlinear Anal. 67:1613-1622.
14. R. Grimmer (1982). Resolvent operators for integral equations in a Banach space. Trans. Am. Math. Soc. 273:333-349.
15. R. Grimmer and A.J. Pritchard (1983). Analytic resolvent operators for integral equations in a Banach space. J. Differential Equations 50:234-259.
16. E. Hernández, M. Pierri, and G. Goncalves (2006). Existence results for an impulsive abstract partial differential equation with state-dependent delay. Comp. Math. Appl. 52:411-420.
17. E. Hernández, M. Rabello, and H.R. Henríuez (2007). Existence of solutions for impulsive partial neutral functional differential equations.J. Math. Anal. Appl. 331:1135-1158.
18. S. Hu and N. Papageorgiou (1997). Handbook of Multivalued Analysis, Volume 1: Theory. Kluwer, Dordrecht.
19. A. Lasota and Z. Opial (1965). An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13:781-786.
20. J. Li, J.J. Nieto, and J. Shen (2007). Impulsive periodic boundary value problems of first-order differential equations. Math. Anal. Appl. 325:226-236.
21. JJ. Nieto (1997). Basic theory for nonresonance impulsive periodic problems of first order. J. Math. Anal. Appl. 205:423-433.
22. JJ. Nieto (2002). Impulsive resonance periodic problems of first order. Appl. Math. Lett. 15:489- 493.
23. Z. Luo, J. Shen, and JJ. Nieto (2005). Antiperiodic boundary value problem for first-order impulsive ordinary differential equations. Comput. Math. Appl. 49:253-261.
24. H. Oka (1995). Integrated resolvent operators. J. Integral Equations 7:193-232.
25. J. Pruss (1983). On resolvent operators for linear integrodifferential equations of Volterra type. J. Integral Equations 5:211-236.
26. C.C. Travis and G.F. Webb (1978). Existence, stability and compactness with α-norm for partial functional differential equations. Trans. Am. Math. Soc. 240:129-143.
27. K. Yosida (1980). Functional Analysis. 6th ed. Springer, Berlin.
28. H. Zhang, L. Chen, and J.J. Nieto (2008). A delayed epidemic model with stage-structure and pulses for pest management strategy. Nonlinear Anal. Real World Appl. 9:1714-1726.