Eigenvalues of the \(p\)-Laplacian in fractal strings with indefinite weights (Q2484191)

The asymptotic behavior of the spectral counting function is studied for the boundary value problem \[ -(\psi_p(u'))'=\lambda r(x)\psi_p(u),\; x\in\Omega, \] with Dirichlet boundary conditions, where \(\Omega\) is a bounded open set in \({\mathbb R}\), \(p>1\), \(\lambda\) is a real spectral parameter, \(\psi_p(s)=| s| ^{p-2}s\), and the weight \(r\) is a given bounded function which may change sign.