| 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 |
| . |
