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Asymptotic Formulas of the Solutions and the Trace Formulas for the Polynomial Pencil of the Sturm-Liouville Operators
Department of Mathematics, Cumhuriyet University, Sivas, Turkey
- 1 Department of Mathematics, Cumhuriyet University, Sivas, Turkey
Applied Mathematics·Volume 07 (2016)·Pages 2411–2417·Published 2 December 2016·DOI10.4236/am.2016.718189
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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.
KeywordsSturm-Liouville EquationAsymptotic Formulas for SolutionsSpectral ParameterEigenvalueBoundary Value ProblemTrace FormulaFractional Integrals and Derivatives
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