Lack of Compactness for Bounded Ω

David G. Costa
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David G. Costa: University of Nevada, Las Vegas, Department of Mathematical Sciences

Chapter 11 in An Invitation to Variational Methods in Differential Equations, 2007, pp 115-124 from Springer

Abstract: Abstract 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

Date: 2007
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DOI: 10.1007/978-0-8176-4536-6_11

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