In this paper the results of some investigations concerning nonlinear elliptic problems in unbounded domains are summarized and the main difficulties and ideas related to these researches are described. The model problem (P) {-Δu + a(x)u = |u|n-2u in Ω, u ∈ H0 1 (ω), where Ω , N ⊆ ℝ ≥ 3, is an unbounded smooth domain, a(x) is a smooth real function defined on Ω, such that a(x) → |x| →+∞ a∞ > 0, p ∈ (2,2N/N-2), is considered and existence and multiplicity results are given under various assumptions on Ω.
Some nonlinear elliptic problems in unbounded domains / Cerami, Giovanna. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 74:1(2006), pp. 47-77. [10.1007/s00032-006-0059-z]
Some nonlinear elliptic problems in unbounded domains
CERAMI, Giovanna
2006-01-01
Abstract
In this paper the results of some investigations concerning nonlinear elliptic problems in unbounded domains are summarized and the main difficulties and ideas related to these researches are described. The model problem (P) {-Δu + a(x)u = |u|n-2u in Ω, u ∈ H0 1 (ω), where Ω , N ⊆ ℝ ≥ 3, is an unbounded smooth domain, a(x) is a smooth real function defined on Ω, such that a(x) → |x| →+∞ a∞ > 0, p ∈ (2,2N/N-2), is considered and existence and multiplicity results are given under various assumptions on Ω.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
