The First Regularized Trace of the Sturm-Liouville Operator With Robin Boundary Conditions
DOI:
https://doi.org/10.5644/SJM.20.01.14Keywords:
Sturm-Liouville operator, regularized trace, differential equations with delayAbstract
This paper deals with the boundary value problem for the operator Sturm-Liouville type $ D^{2}=D^{2}(h, H, q_{1},q_{2},\tau,\varphi)$ generated by
$$-y''(x)+\sum_{i=1}^{2}q_i(x)y(x-i\tau)=\lambda y(x),\,x\in[0, \pi]$$
$$y'(0)-hy(0)=0,\, y'(\pi)+Hy(\pi)=0$$
where $\ds{\frac{\pi}{3}\leq \tau <\frac{\pi}{2}}$,\,\,$ h, H\in R\setminus\{0\}$ and $\lambda $ is a spectral parameter. We assume that $ q_i$, $i=1,2$ are real-valued potential functions from $ L_2 [0, \pi]$. We establish a formula for the first regularized trace of this operator.
2020 Mathematics Subject Classification. 34B09, 34B24, 34L10
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