# Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel

Paweł Wójcik; Michail A. Sheshko; Dorota Pylak; Paweł Karczmarek

Annales UMCS, Mathematica (2012)

- Volume: 66, Issue: 2, page 93-105
- ISSN: 2083-7402

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topPaweł Wójcik, et al. "Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel." Annales UMCS, Mathematica 66.2 (2012): 93-105. <http://eudml.org/doc/268054>.

@article{PawełWójcik2012,

abstract = {In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.},

author = {Paweł Wójcik, Michail A. Sheshko, Dorota Pylak, Paweł Karczmarek},

journal = {Annales UMCS, Mathematica},

keywords = {Singular integral equations; Cauchy-type kernel; multiplicative kernel; logarithmic singularities.; singular integral equations; logarithmic singularities},

language = {eng},

number = {2},

pages = {93-105},

title = {Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel},

url = {http://eudml.org/doc/268054},

volume = {66},

year = {2012},

}

TY - JOUR

AU - Paweł Wójcik

AU - Michail A. Sheshko

AU - Dorota Pylak

AU - Paweł Karczmarek

TI - Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel

JO - Annales UMCS, Mathematica

PY - 2012

VL - 66

IS - 2

SP - 93

EP - 105

AB - In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.

LA - eng

KW - Singular integral equations; Cauchy-type kernel; multiplicative kernel; logarithmic singularities.; singular integral equations; logarithmic singularities

UR - http://eudml.org/doc/268054

ER -

## References

top- [1] Bisplinghoff, R. L., Ashley, H. and Halfman, R. L., Aeroelasticity, Dover Publications, Mineola, 1996.
- [2] Gakhov, F. D., Boundary Value Problems, Nauka, Moscow, 1977. Zbl0449.30030
- [3] Karczmarek, P., Singular integral equation with a multiplicative Cauchy kernel in thehalf-plane, Opuscula Math. 28 (2008), 63-72. Zbl1180.45001
- [4] Karczmarek, P., Pylak, D., Wójcik, P., Singular integral equations with multiplicativeCauchy-type kernels, Fasc. Math. 50 (2013), in press. Zbl1292.45004
- [5] Lifanov, I. K., Singular Integral Equations and Discrete Vortices, VSP, Utrecht, 1996. Zbl0871.65110
- [6] Muskhelishvili, N. I., Singular Integral Equations. Boundary Problems of FunctionTheory and Their Application to Mathematical Physics, Dover Publications, Inc., Mineola, New York, 2008.
- [7] Pylak, D., Approximate solutions of a singular integral equation with Cauchy kernelin the quarter plane, Opuscula Math. 28 (2008), 179-194. Zbl1161.65095
- [8] Pylak, D., Sheshko, M. A., Inversion of singular integrals with Cauchy kernels in thecase of an infinite integration domain, Differ. Equ. 41 (2005), 1297-1310. Zbl1128.45001
- [9] Sheshko, M., Singular Integral Equations with Cauchy and Hilbert Kernels and TheirsApproximated Solutions, TN KUL, Lublin, 2003.
- [10] Sheshko, M. A., Sheshko, S. M., Inversion of singular integrals with multiplicativeCauchy kernel and infinite integration domain, Differ. Equ. 47 (2011), 534-546.[WoS] Zbl1235.45001

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