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In this paper we study the Sobolev trace embedding W1,p([omega]) --&amp;amp;gt;LpV ([delta omega]), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues [lambda]k --&amp;amp;gt; +[infinity] and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article with the study of the second eigenvalue proving that it coincides with the second variational eigenvalue

A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding