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Journal of the London Mathematical Society 2006 74(2):441-452; doi:10.1112/S002461070602309X
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© The London Mathematical Society 2006

POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM WITH STRONG LACK OF COMPACTNESS

Riccardo Molle

Dipartimento di Matematica, Università di Roma ‘Tor Vergata’ Via della Ricerca Scientifica n. 1, 00133 Roma, Italy molle{at}mat.uniroma2.it

Received 28 April 2005.

This paper deals with the lack of compactness in the nonlinear elliptic problem –{Delta} u + u = |u|p–2u in {Omega}, u > 0 in {Omega}, u = 0 on {partial}{Omega}, when {Omega} is un unbounded domain in Rn and 2 < p < 2n/(n–2).

In particular, a domain Formula is provided where non-converging Palais–Smale sequences exist at every energy level. Nevertheless, it is proved that the problem has infinitely many solutions on Formula.


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