On the Jost Solutions of A Class of the Quadratic Pencil of the Sturm-Liouville Equation

In this study we construct new integral representations of Jost-type solutions the quadratic pencil Sturm-Liouville equation with piece-wise constant coefficient on entire real line. Our aim is to express special in form some operators which kernels related potential function equation. This problem technically diffucult due discontinous causes kernel also have a jump discontinuity.