On solvability of a partial integral equation in the space $L_2(\Omega \times \Omega )$

Abstract

In this paper we investigate solvability of a partial integral equation in the space $L_2(\Omega \times \Omega ),$ where $\Omega =[a,b{]}^{\nu }.$ We define a determinant for the partial integral equation as a continuous function on $\Omega$ and for a continuous kernels of the partial integral equation we give explicit description of the solution.

arXiv comment9 pages