Abstract
ABSTRACT The work is devoted to the study of a second‐order differential equation without a lower term, the variable coefficients of which can grow at infinity. The equation is defined on the entire real axis, and its right‐hand side belongs to the non‐Hilbert Lebesgue space. The connections between the coefficients and the requirements for their growth and oscillation are established, ensuring the correct solvability of the equation, the maximal regularity of a solution, and the complete continuity of the resolvent. Based on the obtained coercive estimate and known theorems on general weighted Sobolev spaces, an upper bound is established for the number of Kolmogorov widths of the class of solutions greater than a given positive number.