Abstract

In this paper we give some simple estimates of positive and negative eigenvalues for the inhomogeneous membrane boundary problem $$ -\Delta u=\lambda mu,\quad u\,|_{\partial D=0} $$ if $D\subset R^2$ is a simple connected domain and $m$ is a real bounded function (possibly changing the sign).

Keywords: Inhomogeneous membrane problem, estimation of eigenvalues.

MSC: 35P15, 35J25, 47F05

Pages:  11$-$14     

Volume  48 ,  Issue  1$-$2 ,  1996