TY - JOUR AU - Л.Н.Раджабова, AU - Ф.М.Ахмадов, PY - 2021/12/30 Y2 - 2024/03/29 TI - Explicit solutions of a two-dimensional integral equation of Volterr type with boundary singularity and strongly singular line when the roots of the characteristic equations are real, different and equal JF - BULLETIN OF THE L.N. GUMILYOV EURASIAN NATIONAL UNIVERSITY. Mathematics. Computer science. Mechanics series JA - mathmc VL - 137 IS - 4 SE - DO - 10.32523/bulmathenu.2021/4.1 UR - https://bulmathmc.enu.kz/index.php/main/article/view/97 SP - 6-13 AB - <p>The paper studies a two-dimensional integral equation of Volterra type with singular and strongly singular<br>boundary lines. The solution of a two-dimensional integral equation of the Volterra type with singular kernels is sought in<br>the class of continuous functions that vanish on the boundary lines.<br>In the case when the roots of the characteristic equations are real, different and equal, the parameters of the equations<br>are related to each other in a certain way, depending on the roots of the characteristic equations and the sign of the<br>parameters of the integral equation, explicit solutions of the integral equation are found.<br>It is proved that the solutions of a two-dimensional integral equation, depending on the sign of the parameters, can<br>contain from one to four arbitrary continuous functions. The cases are determined when the solution to the integral<br>equation is unique.</p> ER -