The existence of solutions of some nonlinear integral equations on an unbounded interval

In the first chapter of this work, consisting of four chapters, the general infor-mation on historical developments and usage areas of the integral equations and some definitions about integral equations are given. The place and importance of the thesis study in the literature are emphasized. In the second chapter, some basic definitions, theorems and the concept of me-asure of noncompactness are given to understand other chapters easily and also, Kuratowski, Hausdor˙ and Istrˇatescu measures of noncompactness are menti-oned. Besides, in this chapter, the measures of noncompactness are introduced on some Banach spaces. The definitions of the concepts " Locally attractive " and " Asymptotically stable " are given. In the last part of this chapter, some fixed point theorems associated with measures of noncompactness are handled. The original parts of the study are the third and fourth chapters. In the third chapter, a nonlinear integral equation on an unbounded interval is examined. The suÿcient conditions enabling the existence of at least one solution of this equation in the space BC (R+, R) are given and the asymptotic behavior of the solutions is determined. By giving some examples, the originality and importance of the study are emphasized. In the fourth chapter, the integral equation discussed in the third chapter is handled under the di˙erent conditions. The existence and the asymptotic stability of the solutions of this integral equation are examined by using a fixed point theorem given via the measure of noncompactness. Additionally, some examples explaining the importance and place of the study in literature are introduced. KEYWORDS: Nonlinear integral equations, the space of bounded and continuous functions, Measure of noncompactness, Darbo fixed point theorem, Asymptotically stable solution.