Existence conditions for eigenvalue problems generated by compact multiparameter operators
1984 ◽
Vol 96
(3-4)
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pp. 261-274
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Keyword(s):
SynopsisLet T, V1,…, Vk denote compact symmetric linear operators on a separable Hilbert space H, and write W(λ) = T + λ1V1 + … + λkVk, λ = (λ1, …, λk) ϵ ℝk. We study conditions on the conerelated to solubility of the multiparameter eigenvalue problemwith W(λ)−I nonpositive definite. The main result is as follows.Theorem. If 0 ∉ V, then (*) is soluble for any T. If 0 ∈ V, then there exists T such that (*) is insoluble.We also deduce analogous results for problems involving self-adjoint operators with compact resolvent.
1981 ◽
Vol 33
(1)
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pp. 210-228
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1981 ◽
Vol 91
(1-2)
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pp. 15-30
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2003 ◽
Vol 46
(3)
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pp. 561-573
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1968 ◽
Vol 68
(1)
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pp. 83-93
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1976 ◽
Vol 74
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pp. 135-143
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1996 ◽
Vol 39
(1)
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pp. 119-132
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1987 ◽
Vol 106
(1-2)
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pp. 39-51
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1970 ◽
Vol 22
(1)
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pp. 134-150
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1988 ◽
Vol 31
(1)
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pp. 127-144
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