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A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding. (English) Zbl 1014.35070

The authors study an eigenvalue problem for the \(p\)-Laplacian with a Neumann type boundary condition involving an indefinite weight. The dependence of the first eigenvalue with respect to the weight is investigated. It is then proved that the second eigenvalue coincides with the so-called second variational eigenvalue.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J70 Degenerate elliptic equations
35J20 Variational methods for second-order elliptic equations
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