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Keywords:
non-linear singular integral equation; Schauder's fixed point theorem; Banach space; Hilbert kernel; quasi-linear singular integro-differential equations
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.
References:
[1] Amer, S. M.: Existence results for a class of non-linear singular integral equations with shift. Il Nuovo Cimento B 120 (2005), 313-333. MR 2175853
[2] Amer, S. M.: On the solvability of non-linear singular integral equation and integro-differential equations of Cauchy type (II). Proc. Math. Phys. Soc. Egypt No. 78 (2003), 91-110. MR 2085958
[3] Gakhov, F. D.: Boundary Value Problems. Dover Publ. New York (1990). MR 1106850 | Zbl 0830.30026
[4] Griffel, D. H.: Applied Functional Analysis. John Wiley & Sons New York (1981). MR 0637334 | Zbl 0461.46001
[5] Gusejnov, A. I., Mukhtarov, Kh. Sh.: Introduction to the Theory of Nonlinear Singular Integral Equations. Nauka Moscow (1980), Russian. MR 0591672 | Zbl 0474.45003
[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. DOI 10.1016/j.na.2005.06.043 | MR 2200151
[7] Junghanns, P., Weber, U.: On the solvability of nonlinear singular integral equations. Z. Anal. Anwend. 12 (1993), 683-698. MR 1264861 | Zbl 0790.45004
[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. DOI 10.1002/mma.272 | MR 1857679 | Zbl 1003.45001
[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. DOI 10.1016/S0362-546X(98)00347-2 | MR 1773984 | Zbl 0963.45008
[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. DOI 10.1023/A:1023058024885 | MR 1467554 | Zbl 0906.76076
[11] Ladopoulos, E. G., Zisis, V. A.: Nonlinear singular integral approximations in Banach spaces. Nonlinear Anal., Theory, Methods Appl. 26 (1996), 1293-1299. DOI 10.1016/0362-546X(95)00008-J | MR 1376104 | Zbl 0856.65147
[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
[13] Lusternik, L. A., Sobolev, V. J.: Elements of Functional Analysis. Gordon and Breach Science Publishers New York (1986). MR 0350359
[14] Mikhlin, S. G., Prössdorf, S.: Singular Integral Operators. Akademie-Verlag Berlin (1986). MR 0881386
[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
[16] Pogorzelski, W.: Integral Equations and Their Applications, Vol. 1. Oxford Pergamon Press/PWN Oxford/Warszawa (1966). MR 0201934
[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
[18] L. von Wolfersdorf: On the theory of nonlinear singular integral equations of Cauchy type. Math. Methods Appl. Sci. 7 (1985), 493-517. DOI 10.1002/mma.1670070136 | MR 0827209 | Zbl 0582.45019
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