On a Fourth Order Boundary Value Problem with Periodic and Transmission Conditions

This study investigates the asymptotic expressions of eigenvalues and eigenfunctions for a fourth-order boundary value problem subject to periodic boundary conditions. It is also examined in the problem with transmission boundary conditions at zero. At t=0, one of the transmission boundary conditions have jump discontinuity. Firstly, asymptotic formulas of fundamental solutions are found. The asymptotic formulas of the eigenvalues are computed by the aid of Rouche method. Finally corresponding eigenfunctions to these eigenvalues are presented.