Integral operator and oscillation of second order elliptic equations

Abstract

By using integral operator, some oscillation criteria for second order elliptic differential equation

$$ \sum^d _{i,j=1} D_i[A_{ij}(x)D_jy]+ q(x)f(y)=0, \;x \in \Omega\qquad \eqno{(E)} $$

are established. The results obtained here can be regarded as the extension of the well-known Kamenev theorem to Eq.$(E)$.