A CLASS OF NONLINEAR EIGENVALUE PROBLEMS.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The report considers the nonlinear eigenvalue problem A - Blambdax 0 in a Hilbert space, where A or 0 is compact and Blambda is a polynomial with nonnegative operator coefficients, satisfying B0 0. It is shown that if A and Blambda are in certain operator classes, then there exists an unconditional basis of the Hilbert space consisting of eigenvectors x corresponding to nonnegative eigenvalues lambda. It is also shown that the nonnegative eigenvalues can be characterized by variational principles. Author
- Theoretical Mathematics