Solvability of a nonlinear integral equation of Volterra type.(English)Zbl 1026.45006

The paper investigates a class of Volterra integral equations, in particular their solvability in the space of continuous and bounded functions on $$R_+$$, using the technique associated with measures of noncompactness. The findings are illustrated with several examples.

MSC:

 45G10 Other nonlinear integral equations 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
Full Text:

References:

 [1] Argyros, I.K., Quadratic equations and applications to Chandrasekhar’s and related equations, Bull. austral. math. soc., 32, 275-292, (1985) · Zbl 0607.47063 [2] Banás, J.; Goebel, K., Measures of noncompactness in Banach spaces, Lecture notes in pure and applied mathematics, Vol. 60, (1980), Marcel Dekker New York · Zbl 0441.47056 [3] Banás, J.; Lecko, M.; El-Sayed, W.G., Existence theorems for some quadratic integral equations, J. math. anal. appl., 222, 276-285, (1998) · Zbl 0913.45001 [4] Banás, J.; Rodríguez, J.R.; Sadarangani, K., On a class of urysohn – stieltjes quadratic integral equations and their applications, J. comput. appl. math., 113, 35-50, (2000) · Zbl 0943.45002 [5] Banás, J.; Rodríguez, J.R.; Sadarangani, K., On a nonlinear quadratic integral equation of urysohn – stieltjes type and its applications, Nonlinear anal., 47, 1175-1186, (2001) · Zbl 1042.45502 [6] Banás, J.; Sadarangani, K., Solvability of volterra – stieltjes operator-integral equations and their applications, Comput. math. appl., 41, 1535-1544, (2001) · Zbl 0986.45006 [7] Case, K.M.; Zweifel, P.F., Linear transport theory, (1967), Addison-Wesley Reading, MA · Zbl 0132.44902 [8] Chandrasekhar, S., Radiative transfer, (1950), Oxford University Press London · Zbl 0037.43201 [9] Deimling, K., Nonlinear functional analysis, (1985), Springer Berlin · Zbl 0559.47040 [10] O’Regan, D.; Meehan, M.M., Existence theory for nonlinear integral and integrodifferential equations, (1998), Kluwer Academic Dordrecht · Zbl 0891.45004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.