Asymptotics of the number of eigenvalues of one-term second-order operator equations

摘要

We study one-term operator L acting in the space H 1 = L 2 ( [ 0 , ∞ ) ; H ) $H_{1}=L_{2}([0,infty );H)$ generated by the operator-differential expression L = − d d x ( P ( x ) d d x ) $mathcal{L}=-rac{d}{dx} ( P(x)rac{d}{dx})$ and the boundary condition y ( 0 ) = 0 $y(0)=0$ . We evaluate the asymptotic number of eigenvalues of the operator L under certain conditions.