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

Authors:	Molle Riccardo

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

Abstract:	This paper deals with the lack of compactness in the nonlinearelliptic problem ${Delta}$ u + u = \|u\|^p2u in ${Omega}$ , u > 0in ${Omega}$ , u = 0 on ${partial}$ ${Omega}$ , when ${Omega}$ is un unbounded domain in $R$ ⁿ and 2 <p < 2n/(n2). In particular, a domain is provided where non-converging PalaisSmale sequences existat every energy level. Nevertheless, it is proved that the problemhas infinitely many solutions on .

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