Nonlinear eigenvalue problems governed by a variational inequality of von Karman's type: A degree theoretic approach (Q1327672)

The paper is devoted to the study of a general nonlinear eigenvalue problem governed by a variational inequality: Find \(\lambda^*\in R\), \(u^*\in k\) such that \((F(\lambda^*, u^*), v-u^*) \geq 0\) for each \(v\in k\), where \(k\) is a closed convex subset of an Hilbert space \(X\) and \(F: R\times k\to X\) is a nonlinear mapping. An existence theorem is given. Moreover the authors develop a bifurcation theory for the nonlinear eigenvalue problem defined above and describe some aspects of a spectral theory relative to the variational inequality.