caa a22 4500 605525196 CHVBK 20210128100757.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2479-1 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2479-1 On One Linear Integral Equation with a Coefficient that has Zeros [Elektronische Daten] [D. Shulaia, P. Ghurtskaia] The aim of this paper is to study, in the class of H¨older functions, a linear integral equation with coefficient having two simple zeros in the interval under consideration. Using the theory of singular integral equations, we give the necessary and sufficient conditions for the solvability of this equation under some assumptions on their kernel. Finding a solution is reduced to solving a regular integral equation of the second kind. Springer Science+Business Media New York, 2015 Shulaia D. I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia aut Ghurtskaia P. Georgian Technical University, Tbilisi, Georgia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/6(2015-08-01), 706-722 1072-3374 208:6<706 2015 208 10958 https://doi.org/10.1007/s10958-015-2479-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2479-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shulaia D. I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia aut NATIONALLICENCE 700 1- Ghurtskaia P. Georgian Technical University, Tbilisi, Georgia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/6(2015-08-01), 706-722 1072-3374 208:6<706 2015 208 10958