Geodesic
Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 2.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: Singular integral equations, Cauchy-type kernel, multiplicative kernel, logarithmic singularities 
@article{AUM_2012_66_2_a7,
     author = {W\'ojcik, Pawe{\l} and Sheshko, Michail A. and Pylak, Dorota and Karczmarek, Pawe{\l}},
     title = {Solution of a class of the first kind singular integral equation with multiplicative {Cauchy} kernel},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2012_66_2_a7/}
}
TY  - JOUR
AU  - Wójcik, Paweł
AU  - Sheshko, Michail A.
AU  - Pylak, Dorota
AU  - Karczmarek, Paweł
TI  - Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2012
VL  - 66
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2012_66_2_a7/
LA  - en
ID  - AUM_2012_66_2_a7
ER  - 
%0 Journal Article
%A Wójcik, Paweł
%A Sheshko, Michail A.
%A Pylak, Dorota
%A Karczmarek, Paweł
%T Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2012
%V 66
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2012_66_2_a7/
%G en
%F AUM_2012_66_2_a7
Wójcik, Paweł; Sheshko, Michail A.; Pylak, Dorota; Karczmarek, Paweł. Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 66 (2012) no. 2. http://geodesic.mathdoc.fr/item/AUM_2012_66_2_a7/

[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.

[3] Karczmarek, P., Singular integral equation with a multiplicative Cauchy kernel in the half-plane, Opuscula Math. 28 (2008), 63-72.

[4] Karczmarek, P., Pylak, D., Wójcik, P., Singular integral equations with multiplicative Cauchy-type kernels, Fasc. Math. 50 (2013), in press.

[5] Lifanov, I. K., Singular Integral Equations and Discrete Vortices, VSP, Utrecht, 1996.

[6] Muskhelishvili, N. I., Singular Integral Equations. Boundary Problems of Function Theory 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 kernel in the quarter plane, Opuscula Math. 28 (2008), 179-194.

[8] Pylak, D., Sheshko, M. A., Inversion of singular integrals with Cauchy kernels in the case of an infinite integration domain, Differ. Equ. 41 (2005), 1297-1310.

[9] Sheshko, M., Singular Integral Equations with Cauchy and Hilbert Kernels and Theirs Approximated Solutions, TN KUL, Lublin, 2003.

[10] Sheshko, M. A., Sheshko, S. M., Inversion of singular integrals with multiplicative Cauchy kernel and infinite integration domain, Differ. Equ. 47 (2011), 534-546.