International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 133-140
doi:10.1155/S0161171295000172

A boundary value problem with a discontinuous coefficient and containing a spectral parameter in the boundary condition

Abstract

A singular non-self-adjoint boundary value problem is considered. This problem has a discontinuous coefficient with a spectral parameter in the boundary condition. Some solutions of the eigenvalue equation are given. The discrete spectrum is studied and the resolvent is obtained. Formulation of the adjoint problem is deduced and hence the continuous spectrum of the considered problem is given. Furthermore, the spectrum of the adjoint problem is investigated.