Existence of nondecreasing and continuous solutions for a nonlinear integral equation with supremum in the kernel

Zeitschrift für Analysis und ihre Anwendungen

Volumn 26, Issue 2, 2007, Pages 195-205

  Caballero, J ^a   Lopez B ^a   Sadarangani, K ^a  

^a UNIVERSITY OF LAS PALMAS DE GRAN CANARIA   (Spain)

Author keywords

Fixed point theorem; Measure of noncompactness; Nondecreasing solutions

Indexed keywords

EID: 34547208620     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/1318     Document Type: Article

References (16)

1. Agarwal, R. P., O'Regan, D. and Wong, P. J. Y., Positive Solutions of Differential, Difference and Integral Equations. Dordrecht: Kluwer 1999.
2. Angelov, V. G. and Bainov, D. D., On the functional differential equations with "maximums". Appl. Anal. 16 (1983), 187- 194.
3. Argyros, I. K., Quadratic equations and applications to Chandrasekhar's and related equations. Bull. Austral. Math. Soc. 32 (1985), 275 - 292.
4. Bainov, D. D. and Hristova, S. G., Monotone-iterative techniques of V. Lakshmikantham for a boundary value problem for systems of impulsive differential equations with "supremum". J. Math. Anal. Appl. 172 (1993), 339 - 352.
5. Bainov, D. D., Milusheva, S. D. and Nieto, J. J., Partially multiplicative averaging for impulsive differential equations with supremum. Proc. A. Razdmadze Math. Inst. 110 (1994), 1 - 18.
6. Bainov, D. D. and Mishev, D. P., Oscillation Theory for Neutral Differential Equations with Delay. Bristol: Adam Hilger 1991.
7. Bainov, D. D. and Zahariev, A. I., Oscillating and asymptotic properties of a class of functional differential equations with maxima. Czechoslovak Math. J. 34 (1984), 247 - 251.
8. Banaś, J., Applications of Measures of Noncompactness to Various Problems (in Russian). Zeszyty Nauk. Politech. Rzeszowskiej Mat. Fiz. 34. Rzeszów 1987.
9. Banaś, J. and Goebel, K., Measures of Noncompactness in Banach Spaces. Lecture Notes Pure Appl. Math. 60. New York: Marcel Dekker 1980.
10. Banas, J. and Olszowy, L., Measures of noncompactness related to monotonicity. Comment. Math. 41 (2001), 13 - 23.
11. Banaś, J. and Sadarangani, K., Solvability of Volterra-Stieltjes operatorintegral equations and their applications. Comput. Math. Appl. 41 (2001), 1535 - 1544.
12. Caballero, J., López, B. and Sadarangani, K., On monotonie solutions of an integral equation of Volterra type with supremum. J. Math. Anal. Appl. 305 (2005), 304 - 315.
13. Deimling, K., Nonlinear Functional Analysis. Berlin: Springer 1985.
14. Hu, S., Khavanin, M. and Zhuang, W., Integral equations arising in the kinetic theory of gases. Appl. Anal. 34 (1989), 261 - 266.
15. Meehan, M. M. and O'Regan, D., Existence Theory for Nonlinear Integral and Integro differential Equations. Dordrecht: Kluwer 1998.
16. Myshkis, A. D., On some problems of the theory of differential equations with deviating argument (in Russian). Uspehi Mat. Nauk 32 (1977), 173 - 202.