TITLE:
Asymptotic Formulas of the Solutions and the Trace Formulas for the Polynomial Pencil of the Sturm-Liouville Operators
AUTHORS:
A. Adiloglu Nabiev
KEYWORDS:
Sturm-Liouville Equation, Asymptotic Formulas for Solutions, Spectral Parameter, Eigenvalue, Boundary Value Problem, Trace Formula, Fractional Integrals and Derivatives
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.18,
December
28,
2016
ABSTRACT: This work studies the asymptotic formulas
for the solutions of the Sturm-Liouville equation with the polynomial
dependence in the spectral parameter. Using these asymptotic formulas it is
proved some trace formulas for the eigenvalues of a simple boundary problem
generated in a finite interval by the considered Sturm-Liouville equation.