Bouazizi Wahid

An eigenvalue problem for Sturm-Liouville problems

In this paper, we study theorder of the Dirichlet and Neumann eigenvalues for theSturm-Liouville equation $$-(p(x)y')'+q(x)y=\lambda\rho(x) y.$$ We prove that $\lambda_1\geq\mu_2$ (resp. $\lambda _{1}\leq\mu_2 $) for single-barrier $q$ and single-well $p\rho$ in$[0,1]$ (resp. for single-well $q$ and single-barrier $p\rho$ in $[0,1]$).