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

L. Rajabova, F. M. Ahmadov
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引用次数: 0

Abstract

The paper studies a two-dimensional integral equation of Volterra type with singular and strongly singular boundary lines. The solution of a two-dimensional integral equation of the Volterra type with singular kernels is sought in the class of continuous functions that vanish on the boundary lines. In the case when the roots of the characteristic equations are real, different and equal, the parameters of the equations are related to each other in a certain way, depending on the roots of the characteristic equations and the sign of the parameters of the integral equation, explicit solutions of the integral equation are found. It is proved that the solutions of a two-dimensional integral equation, depending on the sign of the parameters, can contain from one to four arbitrary continuous functions. The cases are determined when the solution to the integral equation is unique.
具有边界奇异和强奇异线的二维Volterr型积分方程,当特征方程的根为实、异、等时的显式解
研究了一类边界奇异和强奇异的二维Volterra型积分方程。寻求一类在边界上消失的连续函数中具有奇异核的二维Volterra型积分方程的解。当特征方程的根是实数、不同且相等时,方程的参数之间存在一定的关系,根据特征方程的根和积分方程参数的符号,求出积分方程的显式解。证明了二维积分方程的解,在参数符号不同的情况下,可以包含1 ~ 4个任意连续函数。当积分方程的解是唯一的情况下确定。
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