In a classical article, Hess and Kato [HK] study the problem $$\left\{ {\begin{array}{*{20}{c}} {Au + \lambda mu = 0} \\ {0 \leqslant u \in D\left( A \right), u \ne 0,} \end{array}} \right.$$ (0.1) where A is a strongly elliptic operator on a bounded open set Ω of R n with Dirichlet boundary conditions and m is a continuous bounded function on Ω. They show that there exists a unique λ > 0 such that the problem (0.1) has a solution.