Positive Eigenfunctions of a Schrödinger Operator
نویسندگان
چکیده
منابع مشابه
Positive Eigenfunctions of a Schrödinger Operator
The paper considers the eigenvalue problem −∆u − αu + λg(x)u = 0 with u ∈ H(R ), u = 0, where α, λ ∈ R and g(x) ≡ 0 on Ω, g(x) ∈ (0, 1] on R \ Ω and lim |x |→+∞ g(x) = 1 for some bounded open set Ω ∈ RN . Given α > 0, does there exist a value of λ > 0 for which the problem has a positive solution? It is shown that this occurs if and only if α lies in a certain interval (Γ, ξ1) and that in this ...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2005
ISSN: 0024-6107
DOI: 10.1112/s0024610705006873