An Inverse Problems for Sturm-Liouville-Type Differential Equation With a Constant Delay
DOI:
https://doi.org/10.5644/SJM.12.1.06Keywords:
Differential operators with delay, inverse problem, Fourier trigonometric coefficientAbstract
The topic of this paper is non-self-adjoint second order differential operators with constant delay generated by $-y''+q(x)y(x-\tau)$ where potential $q$ is complex-valued function, $\tau \in (\frac{\pi}{2},\pi)$ . We establish properties of the spectral characteristics and research the inverse problem of recovering operators from their spectra when $y(0)=y(\pi)=0$. We prove that the delay and the potential is uniquely determined from two spectrum, firstly when $y(0)=y'(\pi)=0$ and secondly when $y(0)=y'(\pi)=0$, of those operators. Also we will construct $q$ and $\tau$.
Downloads
References
Ambarzumjan V., Uber eine Frage der Eigenwerttheorie, Zeitshr.fr Physik, -Bd.53., -S. , 690-695 (1929)
Bayramov A., Ozturk Uslub S., Kizilbudak Caliskan S.,Computation of eigenvalues and eigenfunction of a discontinuous boundary value problem with retarded argument, Appl. Math. Comput. 191 , 592-600(2007)
Borg S., Eine Umkehrung der Sturm-Liouvillschen Eigenwertaufgabe, Acta Math. - Bd.78.No.1. -S , 1-96 (1946)
Chuan-Fu Yang, Trace and inverse problem of a discontinuous Sturm-Liouville operator with retarded argument, J. Math. Anal. Appl. 395,30-41(2012)
Freiling G. and Yurko V., Inverse Sturm-Liouville problems and their applications Nova Science Publishers, Inc.Huntigton, NewYork, (2008)
Freiling G. and Yurko V, Inverse problems for Sturm-Liouville diferential operators with a constant delay, Appl. Math. Lett. 25, No. 11,1999-2004(2012)
Levitan B.M. and Sargsjan I.S., Sturm-Liouville and Dirac Operators, Nauka, Moscow,1988; English transl.:Kluwer Academic Publishers, Dordrecht, (1991)
