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
where \(\Omega \subseteq \mathbb{R}^N \), N ≥ 3, is an unbounded smooth domain, a(x) is a smooth real function defined on Ω, such that \(a(x)\xrightarrow[{|x| \to + \infty }]{}a_\infty > 0,\; p \in \left( {2,\frac{{2N}}{{N - 2}}} \right)\), is considered and existence and multiplicity results are given under various assumptions on Ω.
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Work supported by national research project “Metodi variazionali e topologici nello studio di fenomeni non lineari".
Lecture held in the Seminario Matematico e Fisico on February 28, 2005
Received: June 2006
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Cerami, G. Some Nonlinear Elliptic Problems in Unbounded Domains. Milan j. math. 74, 47–77 (2006). https://doi.org/10.1007/s00032-006-0059-z
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DOI: https://doi.org/10.1007/s00032-006-0059-z