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 ?? (? > 0) of a self-adjoint operator L defined by the following differential expression ?(y)=?(p(x)y?(x))??Q(x)y(x) with the boundary condition y(0) = 0 in the space L2(0,?;H).