Alvino, Angelo; Ferone, Vincenzo; Trombetti, Guido On the properties of some nonlinear eigenvalues. (English) Zbl 0908.35094 SIAM J. Math. Anal. 29, No. 2, 437-451 (1998). Summary: We consider the eigenvalue problem for a nonlinear equation involving the \(p\)-Laplacian with homogeneous Dirichlet conditions. We give some properties 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. Cited in 23 Documents MSC: 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35B45 A priori estimates in context of PDEs 49R50 Variational methods for eigenvalues of operators (MSC2000) 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:\(p\)-Laplacian; Payne-Rayner inequality; symmetrization PDFBibTeX XMLCite \textit{A. Alvino} et al., SIAM J. Math. Anal. 29, No. 2, 437--451 (1998; Zbl 0908.35094) Full Text: DOI