Abstract
SynopsisWe study the self-adjoint eigenvalue problem W(λ)x = 0, (*), in Hilbert space for one equation in two parameters. Hereis bounded below with compact resolvent for each λ = (λ1, λ2). We give necessary and sufficient conditions for the existence of λ so that (*) holds with W(λ)= ≧0 and we investigate the geometry of the set Z0 of such λ. We also discuss higher order solution sets Zi where the ith eigenvalue of W(λ) vanishes, deriving various asymptotic results in a unified fashion.
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