A bound for the error of the Ritz method in the case of the Lidstone problem for a singular differential equation of fourth order

For the Lidstone boundary-value problem
$$ u^{(4)}+q(t)\,u=f(t),\quad0<t<1, $$

$$ u(0)=u''(0)=u(1)=u''(1)=0 $$
conditions of solvability are obtained for nonintegrable functions $q(t)$ and $f(t)$, and a computable error bound for the Ritz method is established. Bibl. – 3 titles.