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On the properties of some nonlinear eigenvalues. (English) Zbl 0908.35094

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.

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
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