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 AM  Vol.7 No.18 , December 2016
Asymptotic Formulas of the Solutions and the Trace Formulas for the Polynomial Pencil of the Sturm-Liouville Operators
A. Adiloglu Nabiev
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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.
Keywords: Sturm-Liouville Equation, Asymptotic Formulas for Solutions, Spectral Parameter, Eigenvalue, Boundary Value Problem, Trace Formula, Fractional Integrals and Derivatives
Cite this paper: Nabiev, A. (2016) Asymptotic Formulas of the Solutions and the Trace Formulas for the Polynomial Pencil of the Sturm-Liouville Operators. Applied Mathematics, 7, 2411-2417. doi: 10.4236/am.2016.718189.
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