This paper deals with the lack of compactness in the nonlinear elliptic problem -Delta u+u = vertical bar u vertical bar(p-2)u in Omega, u > 0 in Omega, u = 0 on delta Omega, when Omega is un unbounded domain in R-n and 2 < p < 2n/(n - 2). In particular, a domain Omega 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 Omega.
Molle, R. (2006). Positive solutions for a nonlinear elliptic problem with strong lack of compactness. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 74(2), 441-452 [10.1112/S002461070602309X].
Positive solutions for a nonlinear elliptic problem with strong lack of compactness
MOLLE, RICCARDO
2006-01-01
Abstract
This paper deals with the lack of compactness in the nonlinear elliptic problem -Delta u+u = vertical bar u vertical bar(p-2)u in Omega, u > 0 in Omega, u = 0 on delta Omega, when Omega is un unbounded domain in R-n and 2 < p < 2n/(n - 2). In particular, a domain Omega 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 Omega.File in questo prodotto:
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