Asymptotic Behaviour of Negative Eigenvalues of an Operator Differential Equation

Abstract

In this work, we find the asymptotic formulas for the sum of the negative eigenvalues smaller than -epsilon (epsilon > 0) of a self-adjoint operator L defined by the following differential expression l(y) = -(p(x)y' (x))' - Q(x) y(x) with the boundary condition y(0) = 0 in the space L-2(0,infinity; H).