Maximal regularity and two‐sided estimates of the approximation numbers of the nonlinear Sturm–Liouville equation solutions with rapidly oscillating coefficients in L₂(ℝ)

Abstract

A theorem on the maximum regularity of solutions of the nonlinear Sturm–Liouville equation with greatly growing and rapidly oscillating potential in the space is proved in this paper. Two‐sided estimates of the Kolmogorov widths of the sets associated with solutions of the nonlinear Sturm–Liouville equation are also obtained. As is known, the obtained estimates give the opportunity to choose approximation apparatus that guarantees the minimum possible error.