Linear elliptic eigenvalue problems involving an indefinite weight
نویسندگان
چکیده
منابع مشابه
Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains.
This paper is concerned with an indefinite weight linear eigenvalue problem in cylindrical domains. We investigate the minimization of the positive principal eigenvalue under the constraint that the weight is bounded by a positive and a negative constant and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the opt...
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This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining t...
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λ0 = λ0(1, P, Ω) := sup{λ ∈ R : ∃u > 0 s.t. (P − λ)u ≥ 0 in Ω}, where 1 is the constant function on Ω, taking at any point x ∈ Ω the value 1. Using the Krein-Rutman theorem, the author proved in [13, 14] generalized maximum principles and anti-maximum principles (in brief, GMPs and AMPs, respectively) for the problem (P − λ)uλ = f 0 in Ω. (1.1) In particular, these GMPs and AMPs (without weight...
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where L is a symmetric elliptic operator and r is a locally integrable function on Rn. If r is of constant sign then this problem leads to a selfadjoint problem in the Hilbert space L2(|r|). In this note we are interested in the case when r takes both positive and negative values on sets of positive measure. Then the spectrum of the problem (1) is not necessarily real any more. Moreover it is n...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1987
ISSN: 0022-247X
DOI: 10.1016/0022-247x(87)90059-x