The equation {Mathematical expression} is considered, where q is bounded below and q(x)→∞ as |x|→∞. Under appropriate conditions on the perturbation term f(x, u) it is shown that given any r>0, (*) has an infinite sequence (λn, r )n ∈ N of eigenvalues, each λn, r being associated with an eigenfunction un,r which satisfies {Mathematical expression}. Information about the behaviour of λn, r for large n is provided. The proofs rely on the compactness of the embedding of a certain weighted Sobolov space in an Lp space; this is proved in §2. © 1993 Hebrew University.
Chiappinelli, R., Edmunds, D.E. (1993). Eigenvalue asymptotics and a nonlinear Schrödinger equation. ISRAEL JOURNAL OF MATHEMATICS, 81(1-2), 179-192 [10.1007/BF02761304].
Eigenvalue asymptotics and a nonlinear Schrödinger equation
CHIAPPINELLI, RAFFAELE;
1993-01-01
Abstract
The equation {Mathematical expression} is considered, where q is bounded below and q(x)→∞ as |x|→∞. Under appropriate conditions on the perturbation term f(x, u) it is shown that given any r>0, (*) has an infinite sequence (λn, r )n ∈ N of eigenvalues, each λn, r being associated with an eigenfunction un,r which satisfies {Mathematical expression}. Information about the behaviour of λn, r for large n is provided. The proofs rely on the compactness of the embedding of a certain weighted Sobolov space in an Lp space; this is proved in §2. © 1993 Hebrew University.
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https://hdl.handle.net/11365/32310
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