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Eigenvalues of elliptic boundary value problems with an indefinite weight function
Transactions of the American Mathematical Society
We consider general selfadjoint elliptic eigenvalue problems (P) Au = Xr(x)u, in an open set O C R*1. Here, the operator A is positive and of order 2m and the "weight" r is a function which changes sign in O and is allowed to be discontinuous. A scalar A is said to be an eigenvalue of (P) if Au = Xru-in the variational sense-for some nonzero u satisfying the appropriate growth and boundary conditions. We determine the asymptotic behavior of the eigenvalues of (P), under suitable assumptions. Indoi:10.1090/s0002-9947-1986-0831201-3 fatcat:kfo4vomccvgeplwjc24rd5pqoi