Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : On calculation of eigenvalues and eigenfunctions of a Sturm-Liouville type problem with retarded argument which contains a spectral parameter in the boundary condition | ịen and Bayramov Journal of Inequalities and Applications 2011 2011 113 http content 2011 1 113 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access On calculation of eigenvalues and eigenfunctions of a Sturm-Liouville type problem with retarded argument which contains a spectral parameter in the boundary condition Erdogan Ẹen and Azad Bayramov Correspondence esen@ Department of Mathematics Faculty of Arts and Science Namik Kemal University 59030 Tekirdag Turkey Springer Abstract In this study a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition and with transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. MSC 2010 34L20 35R10. Keywords differential equation with retarded argument transmission conditions asymptotics of eigenvalues and eigenfunctions 1 Introduction Boundary-value problems for differential equations of the second order with retarded argument were studied in 1-5 and various physical applications of such problems can be found in 2 . The asymptotic formulas for the eigenvalues and eigenfunctions of boundary problem of Sturm-Liouville type for second order differential equation with retarded argument were obtained in 5 . The asymptotic formulas for the eigenvalues and eigenfunctions of Sturm-Liouville problem with the spectral parameter in the boundary condition were obtained in 6 . In the articles 7-9 the asymptotic formulas for the eigenvalues and eigenfunctions of discontinuous Sturm-Liouville problem with transmission conditions and with the boundary conditions which include spectral parameter were obtained. In this article we study the eigenvalues and eigenfunctions of discontinuous boundary-value problem with retarded argument and a spectral parameter in the boundary condition. Namely we consider the .
