| Title:
|
Existence results for non-linear singular integral equations with Hilbert kernel in Banach spaces (English) |
| Author:
|
Saleh, Mohmed H. |
| Author:
|
Amer, Samir M. |
| Author:
|
Ahmed, Marwa H. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
337-349 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A class of non-linear singular integral equations with Hilbert kernel and a related class of quasi-linear singular integro-differential equations are investigated by applying Schauder's fixed point theorem in Banach spaces. (English) |
| Keyword:
|
non-linear singular integral equation |
| Keyword:
|
Schauder's fixed point theorem |
| Keyword:
|
Banach space |
| Keyword:
|
Hilbert kernel |
| Keyword:
|
quasi-linear singular integro-differential equations |
| MSC:
|
45E99 |
| MSC:
|
45F15 |
| MSC:
|
45G05 |
| MSC:
|
45G10 |
| MSC:
|
45J05 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1212.45006 |
| idMR:
|
MR2520834 |
| DOI:
|
10.1007/s10492-009-0021-9 |
| . |
| Date available:
|
2010-07-20T13:12:01Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140369 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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[4] Griffel, D. H.: Applied Functional Analysis.John Wiley & Sons New York (1981). Zbl 0461.46001, MR 0637334 |
| Reference:
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[5] Gusejnov, A. I., Mukhtarov, Kh. Sh.: Introduction to the Theory of Nonlinear Singular Integral Equations.Nauka Moscow (1980), Russian. Zbl 0474.45003, MR 0591672 |
| Reference:
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[6] Heikkilä, S., Reffett, K.: Fixed point theorems and their applications to the theory of Nash equilibria.Nonlinear Anal., Theory, Methods Appl. 64 (2006), 1415-1436. MR 2200151, 10.1016/j.na.2005.06.043 |
| Reference:
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| Reference:
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[8] Junghanns, P., Semmler, G., Weber, U., Wegert, E.: Nonlinear singular integral equations on a finite interval.Math. Methods Appl. Sci. 24 (2001), 1275-1288. Zbl 1003.45001, MR 1857679, 10.1002/mma.272 |
| Reference:
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[9] Ladopoulos, E. G., Zisis, V. A.: Nonlinear finite-part singular integral equations arising in two-dimensional fluid mechanics.Nonlinear Anal., Theory Methods Appl. 42 (2000), 277-290. Zbl 0963.45008, MR 1773984, 10.1016/S0362-546X(98)00347-2 |
| Reference:
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[10] Ladopoulos, E. G., Zisis, V. A.: Existence and uniqueness for nonlinear singular integral equations used in fluid mechanics.Appl. Math. 42 (1997), 345-367. Zbl 0906.76076, MR 1467554, 10.1023/A:1023058024885 |
| Reference:
|
[11] Ladopoulos, E. G., Zisis, V. A.: Nonlinear singular integral approximations in Banach spaces.Nonlinear Anal., Theory, Methods Appl. 26 (1996), 1293-1299. Zbl 0856.65147, MR 1376104, 10.1016/0362-546X(95)00008-J |
| Reference:
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[12] Ladopoulos, E. G.: Non-linear singular integral equations in real elastodynamics by using Hilbert transformations.Nonlinear Anal., Real World Appl. 6 (2005), 531-536. MR 2129562 |
| Reference:
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[13] Lusternik, L. A., Sobolev, V. J.: Elements of Functional Analysis.Gordon and Breach Science Publishers New York (1986). MR 0350359 |
| Reference:
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[14] Mikhlin, S. G., Prössdorf, S.: Singular Integral Operators.Akademie-Verlag Berlin (1986). MR 0881386 |
| Reference:
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[15] Nassr-Eddine Tatar: On the integral inequality with a kernel singular in time and space.J. Inequal. Pure Appl. Math. 4 (2003). MR 2051583 |
| Reference:
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[16] Pogorzelski, W.: Integral Equations and Their Applications, Vol. 1.Oxford Pergamon Press/PWN Oxford/Warszawa (1966). MR 0201934 |
| Reference:
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[17] L. von Wolfersdorf: Class of nonlinear singular integral and integro-differential equations with Hilbert kernel.Zeitschrift Anal. Anwend. 8 (1989), 563-570. MR 1050095, 10.4171/ZAA/375 |
| Reference:
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[18] L. von Wolfersdorf: On the theory of nonlinear singular integral equations of Cauchy type.Math. Methods Appl. Sci. 7 (1985), 493-517. Zbl 0582.45019, MR 0827209, 10.1002/mma.1670070136 |
| . |
