In this work, we investigate a Dirac system which has discontinuities at finite interior points and contains eigenparameter in both boundary transmission conditions. By defining suitable Hilbert space H associated with the problem, generate self-adjoint operator T such that eigenvalues of considered problem coincide those T. We construct fundamental solutions get asymptotic formulas for solutio...

This paper is devoted to investigating the uniform convergence conditions of Fourier series expansions continuous functions in terms eigenfunctions a Sturm-Liouville problem with eigenparameter one boundary on closed interval. Such problems are quite common mathematical physics problems.

In this paper we apply a minmax characterization for nonoverdamped nonlinear eigenvalue problems to a rational eigenproblem governing mechanical vibrations of a tube bundle immersed in an inviscid compressible fluid. This eigenproblem is nonstandard in two respects: it depends rationally on the eigenparameter, and it involves non-local boundary conditions. Comparison results are proved comparin...

Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. In this paper we use the derivative sampling theorem ‘Hermite interpolations’ to compute approximate values of the eigenvalues of Dirac systems with eigenvalue parameter in one or two boundary conditions. We use recently deri...