On Monotonic Solutions of A Nonlinear Integral Equation of Volterra Type
DOI:
https://doi.org/10.15377/2409-5761.2016.03.01.7Keywords:
Nonlinear volterra integral equations, measure of noncompactness, fixed point theoremAbstract
We study a nonlinear integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval. Using a technique associated with measure of noncompactness we prove the existence of the nondecreasing solutions to a nonlinear integral equations of Volterra type in C [0, 1]. We give also one example satisfying the conditions of our main result but not satisfying the conditions of the main result in [1].
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Caballero J, Rocha J and Sadarangani K. On monotonic solutions of an integral equation of Volterra type. Journal of Computational and Applied Mathematics 2005; 174: 119-133. http://dx.doi.org/10.1016/j.cam.2004.04.003 DOI: https://doi.org/10.1016/j.cam.2004.04.003
Agarwal RP, O'Regan D and Wong PJY. Positive Solutions of Differential and Integral Equations. Dordrecht, Kluwer Academic Publishers 1999. http://dx.doi.org/10.1007/978-94-015-9171-3 DOI: https://doi.org/10.1007/978-94-015-9171-3_22
Argyros IK. Quadratic Equations applications to Chandrasekhar's and related equations. Bull Austral Math Soc 1985; 32: 275-292. http://dx.doi.org/10.1017/S0004972700009953 DOI: https://doi.org/10.1017/S0004972700009953
Banas J and Goebel K. Measure of Noncompactness in Banach Spaces. New York, Marcel Dekker 1980.
Banas J and Olszowy L. Measure of Noncompactness related to monotoncity. Comment Math 2001; 41: 13-23.
Banas J and Sadarangani K. Solvabolity of Volterra-Stieltjes operator-integral equations and their applications. Comput Math Applic 2001; 41(12): 1535-1544. http://dx.doi.org/10.1016/S0898-1221(01)00118-3 DOI: https://doi.org/10.1016/S0898-1221(01)00118-3
Deimling K. Nonlinear Functional Analysis. Berlin, Springer- Verlag 1985. http://dx.doi.org/10.1007/978-3-662-00547-7 DOI: https://doi.org/10.1007/978-3-662-00547-7
Hu S, Khavanin M and Zhuang W. Integral equations arising in the kinetic theory of gases. Appl Analysis 1989; 34: 261-266. http://dx.doi.org/10.1080/00036818908839899 DOI: https://doi.org/10.1080/00036818908839899
O'Regan D and Meehan MM. Existence Theory for Nonlinear Integral and Integrodifferential Equations. Dordrecht, Kluwer Academic Publishers 1998. http://dx.doi.org/10.1007/978-94-011-4992-1 DOI: https://doi.org/10.1007/978-94-011-4992-1_2
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