# Article

 Title: Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$ (English) Author: Khachatryan, Aghavard Kh. Author: Khachatryan, Khachatur A. Language: English Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica ISSN: 0231-9721 Volume: 52 Issue: 1 Year: 2013 Pages: 89-100 Summary lang: English . Category: math . Summary: The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$. This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established. (English) Keyword: Wiener–Hopf operator Keyword: Hammerstein–Nemytskii equation Keyword: Caratheodory condition Keyword: one-parameter family of positive solutions Keyword: iteration Keyword: monotonic increasing and bounded solution MSC: 45G05 MSC: 47H30 idZBL: Zbl 1290.45001 idMR: MR3202752 . Date available: 2013-08-02T08:00:42Z Last updated: 2014-07-30 Stable URL: http://hdl.handle.net/10338.dmlcz/143394 . Reference: [1] Arabadjyan, L. G., Yengibaryan, N. B.: Convolution equations and nonlinear functional equations. Itogi nauki i teckniki, Math. Analysis 4 (1984), 175–242 (in Russian). MR 0780564 Reference: [2] Gokhberg, I. Ts., Feldman, I. A.: Convolution Equations and Proections Methods of Solutions. Nauka, Moscow, 1971. MR 0355674 Reference: [3] Khachatryan, A. Kh., Khachatryan, Kh. A.: Existence and uniqueness theorem for a Hammerstein nonlinear integral equation. Opuscula, Mathematica 31, 3 (2011), 393–398. Zbl 1228.45007, MR 2802902, 10.7494/OpMath.2011.31.3.393 Reference: [4] Khachatryan, A. Kh., Khachatryan, Kh. A.: On solvability of a nonlinear problem in theory of income distribution. Eurasian Math. Jounal 2 (2011), 75–88. Zbl 1258.45004, MR 2910832 Reference: [5] Khachatryan, Kh. A.: On one class of nonlinear integral equations with noncompact operator. J. Contemporary Math. Analysis 46, 2 (2011), 71–86. MR 2828824 Reference: [6] Khachatryan, Kh. A.: Some classes of Urysohn nonlinear integral equations on half line. Docl. NAS Belarus 55, 1 (2011), 5–9. MR 2932258 Reference: [7] Kolmogorov, A. N., Fomin, V. C.: Elements of Functions Theory and Functional Analysis. Nauka, Moscow, 1981 (in Russian). Reference: [8] Lindley, D. V.: The theory of queue with a single sever. Proc. Cambridge Phil. Soc. 48 (1952), 277–289. MR 0046597 Reference: [9] Milojevic, P. S.: A global description of solution to nonlinear perturbations of the Wiener–Hopf integral equations. El. Journal of Differential Equations 51 (2006), 1–14. MR 2226924 .

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