Widths of weighted Sobolev classes with restrictions   $f(a)=\dots=f^{(k-1)}(a)=f^{(k)}(b)=\dots=f^{(r-1)}(b)=0$ and spectra of   non-linear differential equations
  In this paper we prove that Kolmogorov widths of weighted Sobolev classes with restrictions $f(a)=\dots=f^{(k-1)}(a)=f^{(k)}(b)=\dots=f^{(r-1)}(b)=0$ in a weighted Lebesgue space and spectral numbers of some non-linear differential equation coincide. Here we suppose that the embedding is compact. 
A.A. Vasil'eva
math.CA math.FA