Asymptotic of eigenvalues and lattice points (Q882721)

The author studies the spectral counting function of the nonlinear eigenvalue problem \[ (\left| u^{\prime }\right| ^{p-2}u^{\prime })^{\prime }= \lambda \left| u\right| ^{p-2}u\text{ in }\Omega \text{ and }u=0\text{ on } \partial \Omega , \] where \(1<p<\infty\), \(\lambda \) is a real parameter and \(\Omega \) is a disjoint union of bounded intervals. He proves that the asymptotic expansion of this function contains a two-term Weyl type. Following the Dirichlet technique for the lattice points problem, he gives a simpler proof and extends previous results to the \(p\)-Laplacian operator. He also obtains similar results for domains of infinite measure.