Convergence of Eigenfunction Expansions for a Boundary Value Problem with Spectral Parameter in the Boundary Conditions. I

Abstract

We consider a spectral problem arising in the description of bending vibrations of a homogeneous rod with a longitudinal force acting in the cross sections, with clamped left end, and with a lumped inertial load at the right end. We give a general characterization of the arrangement of eigenvalues on the real line, study the structure of root subspaces and the oscillation properties of eigenfunctions, and analyze the basis properties of the eigenfunction system of this problem in the space $$L_{p}$$, $$1<p<\infty$$.