Electron. J. Differential Equations, Vol. 2016 (2016), No. 271, pp. 1-15.

Existence and asymptotic behavior of solutions for some nonlinear integral equations on an unbounded interval

Bekir İlhan, İsmet Özdemir

The goal in this paper is to prove an existence theorem for the solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Our investigations will be carried out in the space of continuous and bounded functions on an unbounded interval. The main tools are some techniques in analysis and the Schauder fixed point theorem via measures of noncompactness. Our results extend and improve some known results in the recent literature. Three nontrivial examples explain the generalizations and applications of our results.

Submitted May 30, 2016. Published October 10, 2016.
Math Subject Classifications: 45G10, 47H10, 47H08, 45M99.
Key Words: Nonlinear integral equation; measure of noncompactness; fixed-point theorem.

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Bekir İlhan
Malatya Science High School
44110, Malatya, Turkey
email: bekirilhan@gmail.com
İsmet Özdemir
Faculty of Education, İnönü University
44280, Malatya, Turkey

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