Sur quelques problèmes de transmissions non locaux.

Abstract

The present work is devoted on the one hand, to the study of some transmission problems and it consists mainly in the study a differential equation in a domain that contains one or more discontinuity points, with the presence of the spectral parameter in the differential equation and also in at least one of the initial conditions and one of the transmission conditions. We obtained important results on the asymptotic behavior of eigenvalues and eigenvectors and even the asymptotic behavior of the norm of the Eigen function. On the other hand, we present some inequalities of the integral type.