Existence results for Urysohn integral inclusions involving the Henstock integral

Journal of Mathematical Analysis and Applications

Volumn 336, Issue 1, 2007, Pages 44-53

  Satco, B ^a  

^a STEFAN CEL MARE UNIVERSITY OF SUCEAVA   (Romania)

Author keywords

Henstock (set valued) integral; Kamke function; Urysohn integral inclusion

Indexed keywords

EID: 34547135177     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.02.050     Document Type: Article

References (22)

1. Ambrosetti A. Un teorema di existenza per le equazioni differenziali negli spazi di Banach. Rend. Sem. Univ. Padova 39 (1967) 349-360
2. Cao S.S. The Henstock integral for Banach-valued functions. SEA Bull. Math. 16 (1992) 35-40
3. Castaing C., and Valadier M. Convex Analysis and Measurable Multifunctions. Lecture Notes in Math. vol. 580 (1977), Springer-Verlag, Berlin
4. ′ = f (t, x) and Henstock-Kurzweil integrals. Differential Integral Equations 4 4 (1991) 861-868
5. Cichón M., Kubiaczyk I., and Sikorska A. The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem. Czechoslovak Math. J. 54 129 (2004) 279-289
6. Di Piazza L. Kurzweil-Henstock type integration on Banach spaces. Real Anal. Exchange 29 2 (2003/2004) 543-556
7. Di Piazza L., and Musial K. A decomposition theorem for compact-valued Henstock integral. Monatsh. Math. 148 2 (2006) 119-126
8. Di Piazza L., and Musial K. Set-valued Kurzweil-Henstock-Pettis integral. Set-Valued Anal. 13 2 (2005) 167-179
9. Federson M., and Bianconi R. Linear integral equations of Volterra concerning Henstock integrals. Real Anal. Exchange 25 1 (1999/2000) 389-418
10. Federson M., and Táboas P. Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals. Nonlinear Anal. 50 3 (2002) 389-407
11. Fremlin D.H., and Mendoza J. On the integration of vector-valued functions. Illinois J. Math. 38 1 (1994) 127-147
12. Gordon R.A. The Integrals of Lebesgue, Denjoy, Perron and Henstock. Grad. Stud. in Math. vol. 4 (1994), Amer. Math. Soc., Providence, RI
13. Heinz H.P. On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions. Nonlinear Anal. 7 (1983) 1351-1371
14. Michael E. Continuous selection I. Ann. of Math. 63 (1956) 361-381
15. Mitchell A.A., and Smith C. An existence theorem for weak solutions of differential equations in Banach spaces. Nonlinear Equations in Abstract Spaces. Proc. Internat. Sympos., Univ. Texas, Arlington, TX, 1977 (1978), Academic Press, New York 387-403
16. Mönch H. Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlinear Anal. 4 (1980) 985-999
17. O'Regan D., and Precup R. Fixed point theorems for set-valued maps and existence principles for integral inclusions. J. Math. Anal. Appl. 245 (2000) 594-612
18. O'Regan D., and Precup R. Existence criteria for integral equations in Banach spaces. J. Inequal. Appl. 6 (2001) 77-97
19. Satco B. Second order three boundary value problem in Banach spaces via Henstock and Henstock-Kurzweil-Pettis integral. J. Math. Anal. Appl. 332 (2007) 919-933
20. Satco B. Volterra integral inclusions via Henstock-Kurzweil-Pettis integral. Discuss. Math. Differ. Incl. Control Optim. 26 (2006) 87-101
21. Schwabik S. The Perron integral in ordinary differential equations. Differential Integral Equations 6 4 (1993) 863-882
22. Sikorska-Nowak A. Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals. Demonstratio Math. 35 1 (2002) 49-60