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.
@article{bwmeta1.element.ojs-doi-10_17951_a_2012_66_2_93-105,
author = {Pawe\l\ W\'ojcik and Michail A. Sheshko and Dorota Pylak and Pawe\l\ Karczmarek},
title = {Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {66},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2012_66_2_93-105}
}
Paweł Wójcik; Michail A. Sheshko; Dorota Pylak; Paweł Karczmarek. Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 66 (2012) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2012_66_2_93-105/
Bisplinghoff, R. L., Ashley, H. and Halfman, R. L., Aeroelasticity, Dover Publications, Mineola, 1996.
Gakhov, F. D., Boundary Value Problems, Nauka, Moscow, 1977.
Karczmarek, P., Singular integral equation with a multiplicative Cauchy kernel in the half-plane, Opuscula Math. 28 (2008), 63-72.
Karczmarek, P., Pylak, D., Wójcik, P., Singular integral equations with multiplicative Cauchy-type kernels, Fasc. Math. 50 (2013), in press.
Lifanov, I. K., Singular Integral Equations and Discrete Vortices, VSP, Utrecht, 1996.
Muskhelishvili, N. I., Singular Integral Equations. Boundary Problems of Function Theory and Their Application to Mathematical Physics, Dover Publications, Inc., Mineola, New York, 2008.
Pylak, D., Approximate solutions of a singular integral equation with Cauchy kernel in the quarter plane, Opuscula Math. 28 (2008), 179-194.
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.
Sheshko, M., Singular Integral Equations with Cauchy and Hilbert Kernels and Theirs Approximated Solutions, TN KUL, Lublin, 2003.
Sheshko, M. A., Sheshko, S. M., Inversion of singular integrals with multiplicative Cauchy kernel and infinite integration domain, Differ. Equ. 47 (2011), 534-546.