## REGULARIZED TRACE FORMULA FOR STURM-LIOUVILLE PROBLEM WITH RETARDED ARGUMENT AND QUADRATICALLY EIGENPARAMETER-DEPENDENT BOUNDARY CONDITION

## REGULARIZED TRACE FORMULA FOR STURM-LIOUVILLE PROBLEM WITH RETARDED ARGUMENT AND QUADRATICALLY EIGENPARAMETER-DEPENDENT BOUNDARY CONDITION

*F. Hira, N. Altınışık*

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## Abstract

In this paper, a regularized trace formula for a discontinuous Sturm-Liouville equation with retarded argument is obtained for the case in which the spectral parameter occurs linearly in the equation and one of the boundary conditions and quadratically in the other one. The contour integration method is used to obtain that trace formula.

## Keywords

Di erential equation with retarded argument, trace formula, asymptotics of eigenvalues.