POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM WITH STRONG LACK OF COMPACTNESS
Riccardo Molle · Journal of the London Mathematical Society · 2006
This paper deals with the lack of compactness in the nonlinear elliptic problem −Δ u + u = |u|p−2u in Ω, u > 0 in Ω, u = 0 on ∂Ω, when Ω is un unbounded domain in ℝn and 2 < p < 2n/(n−2). In particular, a domain Ω̃ 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 Ω̃.