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On the boundary value problem for the Sturm–Liouville equation with the discontinuous coefficient |
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| Authors: | A Adiloglu Nabiev RKh Amirov |
| Institution: | 1. Department of Secondary Science and Mathematics Education, Faculty of Education, Cumhuriyet University, , 58140 Sivas, Turkey;2. Department of Mathematics, Faculty of Science, Cumhuriyet University, , 58140 Sivas, Turkey |
| Abstract: | We consider a boundary value problem for the Sturm–Liouville equation with piecewise‐constant leading coefficient. We prove that some integral representations for the solutions of the considered equation can be obtained by using classical transformation operators for the Sturm–Liouville operator at the end points of a finite interval. We also investigate the spectral characteristics of the boundary value problem, prove the completeness and expansion theorem. Copyright © 2012 John Wiley & Sons, Ltd. |
| Keywords: | Sturm– Louville equation boundary value problems spectral analysis of ordinary differential operators transformation operator integral representation asymptotic formulas for eigenvalues expansion formula |