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Normalized eigenvectors for nonlinear abstract and elliptic operators. (English) Zbl 0931.47050

The authors study the eigenvalue problem \(Au= C(\lambda,u)\), where \(A\) is of type \((S)_+\), \(m\)-accretive, or maximal monotone, while \(C\) is continuous and bounded or compact. Particular emphasis is laid on the existence of eigenvectors with special normalization conditions which are natural in view of applications to elliptic boundary value problems.

MSC:

47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
47H05 Monotone operators and generalizations
35J60 Nonlinear elliptic equations
47F05 General theory of partial differential operators
47H11 Degree theory for nonlinear operators
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