On the uniform convergence of spectral expansions for a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter (Q662465)

A spectral problem with spectral parameter in a boundary condition, usually arising when modeling heat transfer in a homogeneous rod with a linear relation between the heat flux and temperature at one end point and with lumped heat capacity at the other end point, is investigated. Taking into account that the problem does not have zero eigenvalues, the associated eigenfunctions are given and the uniform convergence of expansions in eigenfunctions on the interval \([0,1] \) is proven.