Existence, uniqueness and data dependence for the solutions of some integro-differential equations of mixed type in Banach space

Zeitschrift für Analysis und ihre Anwendungen

Volumn 23, Issue 1, 2004, Pages 205-216

  Muresan V ^a  

^a TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

Author keywords

Fixed points; Integro differential equations; Picard operators; Weakly Picard operators

Indexed keywords

EID: 17044445437     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/1194     Document Type: Article

References (22)

1. Aman, H.: On the number of solutions of nonlinear equations in ordered Banach spaces. J. Funct. Anal. 11 (1972), 346-384.
2. Buicǎ, A.: Existence and continuous dependence of solutions of some functional-differential equations. Preprint. Cluj-Napoca: Babeş-Bolyai Univ. (Romania), Seminar on Fixed Point Theory, Preprint 3 (1995), 1-13.
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 of approximate solution to abstract nonlocal Cauchy problem. J. Appl. Math. & Stoch. Anal. 5 (1992), 363-374.
5. Byszewski, L.: Differential and Functional-Differential Problems with Nonlocal Conditions (in Polish; Cracow Univ. Techn. Monograph: Vol. 184). Cracow: Univ. Techn. 1995.
6. Byszewski, L. and V. Lakshmikantham: Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Appl. Anal. 40 (1991), 11-19.
7. Byszewski, L. and A. Tabor: An application of the Kuratowski measure of noncompactness to an investigation of the existence of solutions of an abstract integrodifferential problem. Nonlin. Studies 6 (1999), 111-122.
8. Du, S. W. and V. Lakshmikantham: Monotone iterative technique for differential equations in a Banach space. J. Math. Anal. Appl. 87 (1982), 454-459.
9. Guo Dajun: Ordinary Differential Equations in Abstract Spaces (in Chinese) Jiuan Shandong Sci. and Tech. Press 1985.
10. Guo Dajun: Solutions of nonlinear integrodifferential equations of mixed type in Banach spaces. J. Appl. Math. Simul. 2 (1989), 1-11.
11. Guo Dajun and V. Lakshmikantham: Nonlinear Problems in Abstract Cones. Boston - New York: Acad. Press 1988.
12. Lakshmikantham, V. and S. Leela: Nonlinear Differential Equations in Abstract Spaces. Oxford et al.: Pergamon Press 1981.
13. Lakshmikantham, V., Bainov, D. D. and P. S. Simeonov: Theory of Impulsive Differential Equations. Singapore: World Science 1989.
14. Liu Wei-an: Solutions of nonlinear integrodifferential equations of mixed type with impulses in Banach spaces. Math. Aplicata, Jingyong Shuxue Math. Appl. 9 (1996), 58-62.
15. Mureşan, V.: Differential Equations with Affine Modification of the Argument (in Romania). Cluj-Napoca (Romania): Transilvania Press 1997.
16. Petruşel, A.: Fredholm-Volterra integral equations and Maia's theorem. Preprint. Cluj-Napoca (Romania): Babeş-Boyai Univ., Seminar on Fixed Point Theory, Preprint 3 (1988), 79-82.
17. Rus, I. A.: Metrical Fixed Point Theorems. Univ. of Cluj-Napoca (Romania) 1979.
18. Rus, I. A.: Picard mappings: results and problems. Preprint. Cluj-Napoca: Babeş-Bolyai Univ., Seminar on Fixed Point Theory, Preprint 6 (1987), 55-64.
19. Rus, I. A.: Weakly Picard mappings. Comment. Math. Univ. Carolinae 34 (1993), 769-773.
20. Rus, I. A.: Picard operators and applications. Preprint. Cluj-Napoca (Romania): Babeş,-Bolyai Univ., Seminar on Fixed Point Theory, Preprint 3 (1996).
21. Rus, I. A.: Weakly Picard operators and applications. Cluj-Napoca (Romania): Babeş,-Bolyai Univ., Seminar on Fixed Point Theory 2 (2000), 41-57.
22. Rus, I. A. and S. Mureşan: Data dependence of the fixed points set of some weakly Picard operators. In: Proc. Itinerant Seminar (Elena Popoviciu editor, Srima Publishing House), Cluj-Napoca (Romania): Babeş-Bolyai Univ. 2000, pp. 201-207.