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Genericity of the existence of infinitely many solutions for a class of semilinear elliptic equations in Rn

Allessio, Francesca; Caldiroli, Paolo; Montecchiari, Piero (1998), Genericity of the existence of infinitely many solutions for a class of semilinear elliptic equations in Rn, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, 27, 1, p. 47-68

Type
Article accepté pour publication ou publié
External document link
http://www.numdam.org/item?id=ASNSP_1998_4_27_1_47_0
Date
1998
Journal name
Annali della Scuola Normale Superiore di Pisa. Classe di Scienze
Volume
27
Number
1
Publisher
Scuola Normale Superiore di Pisa
Pages
47-68
Metadata
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Author(s)
Allessio, Francesca
Caldiroli, Paolo
Montecchiari, Piero
Abstract (EN)
We show, by variational methods, that there exists a set A open and dense in {a ∈ L∞(RN) : liminf|x|→∞ a(x) ≥ 0} such that if a ∈ A then the problem −∆u + u = a(x)|u| p−1u, u ∈ H1(RN), with p subcritical (or more general nonlinearities), admits infinitely many solutions.
Subjects / Keywords
Semilinear elliptic equations; locally compact case; minimax arguments; multiplicity of solutions; genericity