Anti-maximum Principles for Indefinite-weight Elliptic Problems
نویسنده
چکیده
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) hold true in nonsmooth, unbounded domains, and for operators with coefficients which may blow up in a neighborhood of infinity in Ω. The GMP in [14] reads roughly that under some ‘smallness’ conditions on uλ, if λ < λ0, and uλ satisfies Equation (1.1),
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