Abstract
We study the following nonlinear elliptic system of Lane–Emden type
where \({\lambda \in \mathbb{R}}\). If \({\lambda \geq 0}\) and \({\Omega}\) is an unbounded cylinder, i.e., \({\Omega = \tilde \Omega \times \mathbb{R}^{N-m} \subset \mathbb{R}^{N}}\), \({N - m \geq 2, m \geq 1}\), existence and multiplicity results are proved by means of the Principle of Symmetric Criticality and some compact imbeddings in partially spherically symmetric spaces. We are able to state existence and multiplicity results also if \({\lambda \in \mathbb{R}}\) and \({\Omega}\) is a bounded domain in \({\mathbb{R}^{N}, N \geq 3}\). In particular, a good finite dimensional decomposition of the Banach space in which we work is given.
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Partially supported by M.I.U.R. Research Project PRIN 2009 “Metodi variazionali e topologici nello studio dei fenomeni non lineari".
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Barile, S., Salvatore, A. Existence and Multiplicity Results for Some Elliptic Systems in Unbounded Cylinders. Milan J. Math. 81, 99–120 (2013). https://doi.org/10.1007/s00032-013-0201-7
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DOI: https://doi.org/10.1007/s00032-013-0201-7