Accession Number : AD0662738

Title :   A CLASS OF NONLINEAR EIGENVALUE PROBLEMS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Turner,R. E. L.

Report Date : AUG 1967

Pagination or Media Count : 44

Abstract : The report considers the nonlinear eigenvalue problem (A - B(lambda))x = 0 in a Hilbert space, where A = or > 0 is compact and B(lambda) is a polynomial with nonnegative operator coefficients, satisfying B(0) = 0. It is shown that if A and B(lambda) 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)

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), HILBERT SPACE, VECTOR SPACES, POLYNOMIALS, OPERATORS(MATHEMATICS), COMPLEX NUMBERS, INEQUALITIES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE