On Asymptotics of the Sum of the Fourth Power of the Negative Eigenvalues of the Singular Sturm-Liouville Operator

Abstract

In this study, we obtain the asymptotic formula for the sum of fourth power of the negative eigenvalues of the operator , which we created with the differential expression and boundary condition in the space . It is known that the operator is self-adjoint, semibounded below, and the negative part of its spectrum is discrete. is self-adjoint, semibounded below, and the negative part of its spectrum is discrete. Additionally, there are some asymptotic formulas for the number of negative eigenvalues of the operator. Our result applies to a class of mathematical physics equations.