Abstract
In this paper, we consider a class of degenerate elliptic equations with arbitrary power degeneration. The issues about the existence, uniqueness, and smoothness of solutions of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration are studied. The two-sided estimates for singular numbers (s-numbers) are obtained. Note that estimates of singular numbers (s-numbers) show the rate of approximation of the found solutions by finite-dimensional subspaces. Here, we also obtain estimates for the eigenvalues. We note that, in this paper, apparently, two-sided estimates of singular numbers (s-numbers) for degenerate elliptic operators are obtained for the first time. At the end of the paper, a symmetric operator is considered, i.e., a self-adjoint case.