On the Properties of Some Nonlinear Eigenvalues
Angelo Alvino, Vincenzo Ferone, Guido Trombetti · SIAM Journal on Mathematical Analysis · 1998
We consider the eigenvalue problem for a nonlinear equation involving the p-Laplacian with homogeneous Dirichlet conditions. We give someproperties of the first eigenvalue and of the corresponding eigenfunction. In particular we prove inequalities similar to the well-known Payne--Rayner inequality, which holds in the linear case.