On the Jost Solutions of A Class of the Quadratic Pencil of the Sturm-Liouville Equation
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 of the quadratic pencil of the Sturm-Liouville equation with the piece-wise constant coefficient on the entire real line. Our aim is to express the special solutions of the Sturm-Liouville quadratic pencil in the form of some integral operators which kernels is related with the potential function of the Sturm-Liouville equation. This problem is technically diffucult due to the discontinous coefficient which causes the kernel function to also have a jump discontinuity.
Keywords:
Sturm-Liouville equation, operator pencil, transformation operator diferantial equation with discontinuous cofficients, Jost solution,
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- Yayın Aralığı: Yılda 3 Sayı
- Başlangıç: 2006
- Yayıncı: Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi