In this paper a necessary and sufficient condition for the existence of negative eigenvalues for the problem-Δu - λu=μα(x)|u|p-2u in Ω u|∂Ω=0 is given. Here Ω ⊂Rn is supposed a smooth bounded domain, α ≢ 0 a bounded nonnegative function, λ ∈ (λ1, λ2), λ1 and λ1 being the first and the second eigenvalue of - Δ in Ω with zero Dirichlet boundary data, p≥2 and, if n ≥ 3, p < 2n|(n-2). Moreover in the linear case (p=2) a uniqueness result is proved
A note on a nonlinear eigenvalue problem / Cerami, Giovanna. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 150:1(1988), pp. 119-128. [10.1007/BF01761465]
A note on a nonlinear eigenvalue problem
Giovanna Cerami
1988-01-01
Abstract
In this paper a necessary and sufficient condition for the existence of negative eigenvalues for the problem-Δu - λu=μα(x)|u|p-2u in Ω u|∂Ω=0 is given. Here Ω ⊂Rn is supposed a smooth bounded domain, α ≢ 0 a bounded nonnegative function, λ ∈ (λ1, λ2), λ1 and λ1 being the first and the second eigenvalue of - Δ in Ω with zero Dirichlet boundary data, p≥2 and, if n ≥ 3, p < 2n|(n-2). Moreover in the linear case (p=2) a uniqueness result is provedFile in questo prodotto:
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