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

摘要

In this paper we prove that Kolmogorov widths of weighted Sobolev classeswith restrictions $f(a)=\dots=f^{(k-1)}(a)=f^{(k)}(b)=\dots=f^{(r-1)}(b)=0$ ina weighted Lebesgue space and spectral numbers of some non-linear differentialequation coincide. Here we suppose that the embedding is compact.