On a boundary value problem with spectral parameter quadratically contained in the boundary condition

Mammedzadeh G. S.

Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, vol.42, no.1, pp.141-150, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2022
  • Journal Name: Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.141-150
  • Keywords: asymptotics, diffusion equation, eigenvalues, nonseparated boundary conditions
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

A boundary value problem generated on an interval by a diffusion equation with real coefficients and nonseparated boundary conditions is considered. One of these boundary conditions includes the quadratic function of the spectral parameter. Some spectral properties of the boundary value problem are studied. It is proved that the eigenvalues are real and nonzero and that there are no associated functions to the eigenfunctions, and an asymptotic formula for the spectrum of the problem is derived.