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Existence of solutions of a nonlinear integral equation on an unbounded interval. (English) Zbl 1190.47090
In this paper, the authors investigate a nonlinear integral equation of Volterra type on an unbounded interval. They show that, under some assumptions, the equation has solutions belonging to the space of bounded and continuous functions on +. The main tool used in this study is the technique associated with measures of noncompactness. The result obtained in this paper generalizes several ones obtained earlier by J. Banas and B. Rzepka [“On existence and asymptotic stability of solutions of a nonlinear integral equation”, J. Math. Anal. Appl. 284, No. 1, 165–173 (2003; Zbl 1029.45003)], Z. Liu and S. M. Kang [“Existence and asymptotic stability of solutions to a functional-integral equation”, Taiwanese J. Math. 11, No. 1, 187–196 (2007; Zbl 1145.45003)].
MSC:
47N20Applications of operator theory to differential and integral equations
47H09Mappings defined by “shrinking” properties
45G10Nonsingular nonlinear integral equations
45D05Volterra integral equations