  The aim of this study is to find asymptotic expressions of eigenvalues and
eigenfunctions of a discontinuous boundary-value problem with retarded argument
which contains a spectral parameter in the boundary condition. Applications of
differential equations with retarded argument can be encountered in the theory
of selfoscillatory systems, in the study of problems connected with combustion
in rocket engines, in a number of problems in economics, biophysics, and many
other fields. The problems in these areas can be solved reducing differential
equations with retarded argument. In this study discontinuous boundary-value
problem with retarded argument which contains a spectral parameter in the
boundary condition were investigated and asymptotic formulas were obtained for
eigenvalues and eigenfunctions for using areas which mentioned above
