Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces

Journal of Applied Mathematics

Volumn 2007, Issue , 2007, Pages

  Sikorska Nowak, Aneta ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41849119072     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2007/31572     Document Type: Article

References (25)

1. S. S. Cao, "The Henstock integral for Banach-valued functions," Southeast Asian Bulletin of Mathematics, vol. 16, no. 1, pp. 35-40, 1992.
2. V. G. Celidze and A. G. Džvaršeǐšvili, Theory of the Denjoy Integral and Some of Its Applications, Tbilis. Gos. Univ., Tbilisi, Russia, 1978.
3. R. A. Gordon, The Integrals of Lebesgue, Denjoy, Perron, and Henstock, vol. 4 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1994.
4. R. Henstock, The General Theory of Integration, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, NY, USA, 1991.
5. P. Y. Lee, Lanzhou Lectures on Henstock Integration, vol. 2 of Real Analysis, World Scientific, Teaneck, NJ, USA, 1989.
6. T. S. Chew, "On Kurzweil generalized ordinary differential equations," Journal of Differential Equations, vol. 76, no. 2, pp. 286-293, 1988.
7. T. S. Chew and F. Flordeliza, "On x′ = f (t,x) and Henstock-Kurzweil integrals," Differential Integral Equations, vol. 4, no. 4, pp. 861-868, 1991.
8. I. Kubiaczyk and A. Sikorska-Nowak, "Differential equations in Banach space and Henstock-Kurzweil integrals," Discussiones Mathematicae. Differential Inclusions, vol. 19, no. 1-2, pp. 35-43, 1999.
9. J. Kurzweil, "Generalized ordinary differential equations and continuous dependence on a parameter," Czechoslovak Mathematical Journal, vol. 7, no. 82, pp. 418-449, 1957.
10. A. Sikorska-Nowak, "Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals," Demonstratio Mathematica, vol. 35, no. 1, pp. 49-60, 2002.
11. R. P. Agarwal, M. Meehan, and D. O'Regan, "Positive solutions of singular integral equations - a survey," Dynamic Systems and Applications, vol. 14, no. 1, pp. 1-37, 2005.
12. R. P. Agarwal, M. Meehan, and D. O'Regan, Nonlinear Integral Equations and Inclusions, Nova Science Publishers, New York, NY, USA, 2001.
13. R. P. Agarwal and D. O'Regan, "Existence results for singular integral equations of fredholm type," Applied Mathematics Letters, vol. 13, no. 2, pp. 27-34, 2000.
14. S. Krzyśka, "On the existence of continuous solutions of Urysohn and Volterra integral equations in Banach spaces," Demonstratio Mathematica, vol. 28, no. 2, pp. 353-360, 1995.
15. M. Meehan and D. O'Regan, "Existence theory for nonlinear Volterra integrodifferential and integral equations," Nonlinear Analysis: Theory, Methods & Applications, vol. 31, no. 3-4, pp. 317-341, 1998.
16. D. O'Regan, "Existence results for nonlinear integral equations," Journal of Mathematical Analysis and Applications, vol. 192, no. 3, pp. 705-726, 1995.
17. D. O'Regan and M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, vol. 445 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, The Netherlands, 1998.
18. H. Mönch, "Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces," Nonlinear Analysis: Theory, Methods & Applications, vol. 4, no. 5, pp. 985-999, 1980.
19. J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, vol. 60 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1980.
20. A. Ambrosetti, "Un teorema di esistenza per le equazioni differenziali negli spazi di Banach," Rendiconti del Seminario Matematico della Università di Padova, vol. 39, pp. 349-361, 1967.
21. R. A. Gordon, "Riemann integration in Banach spaces," The Rocky Mountain Journal of Mathematics, vol. 21, no. 3, pp. 923-949, 1991.
22. G. Ye, P. Y. Lee, and C. Wu, "Convergence theorems of the Denjoy-Bochner, Denjoy-Pettis and Denjoy-Dunford integrals," Southeast Asian Bulletin of Mathematics, vol. 23, no. 1, pp. 135-143, 1999.
23. A. P. Solodov, "On conditions for the differentiability almost everywhere of absolutely continuous Banach-valued functions," Moscow University Mathematics Bulletin, vol. 54, no. 4, pp. 29-32, 1999.
24. R. H. Martin Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Robert E. Krieger, Melbourne, Fla, USA, 1987.
25. A. Alexiewicz, Functional Analysis, PWN, Warsaw, Poland, 1969.