Some estimations of positive and negative eigenvalues. (English) Zbl 0942.35123

Dostanić, M.

Mat. Vesn. 48, No. 1-2, 11-14 (1996).

The author gives some simple estimates of positive and negative eigenvalues for the inhomogeneous membrane boundary problem \[ -\Delta u=\lambda mu ,\qquad u|_{\partial D} =0 \] where \(D\subset \mathbb{R}^2\) is a simple connected domain and \(m\) is a real bounded function on \(D\).

Reviewer: Miroljub Jevtić (Beograd)

MSC:

35P15	Estimates of eigenvalues in context of PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

eigenvalues; inhomogeneous membrane boundary problem