An eigenvalue problem with singularity for fourth order ordinary differential equation
The paper deals with the following eigenvalue problem \[ (pu'')''+qu= \lambda u, \quad 0<x<1, \qquad (pu'')''(0) = \lambda u(0), \quad u''(0) = u(1) = u'(1) = 0. \] The author proves the existence of a countable set of eigenvalues. The arguments are essentially based on the weak formulation of the problem.
scientific article; zbMATH DE number 1369977