Lack of Compactness for Bounded Ω
David G. Costa · Birkhäuser Boston eBooks · 2007
In this chapter we present a simple situation of a variational problem on a bounded domain Ω ⊂ ℝ N for which the corresponding functional does not satisfy the Palais-Smale condition (PS)c at certain levels c ∈ ℝ. We are referring to the so-called strongly resonant problems, a terminology introduced in Bartolo-Benci-Fortunato [8] for a resonant problem where the nonlinearity g(s) was such that lim|s|→∞ g(s) = 0 and lim|s|→∞ G(s) = β < ∞. Such problems did not fall under the Landesman-Lazer [49] or the Ahmad-Lazer-Paul