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 |

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Category: | math |

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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 |

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Date available: | 2013-08-02T08:00:42Z |

Last updated: | 2014-07-30 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/143394 |

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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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