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.