Authors 
: 

Document type 
: 
Article de périodique (Journal article) – Article de recherche

Abstract 
: 
We study the semilinear elliptic equation Delta u=lambdau(q2)u+muu(p2)u in an open bounded domain Omega subset of R(N) with Dirichlet boundary conditions; here 1 < q < 2 < p < 2*. Using variational methods we show that for lambda > 0 and mu is an element of R arbitrary there exists a sequence (upsilon(k)) of solutions with negative energy converging to 0 as k > infinity. Moreover, for mu > 0 and lambda arbitrary there exists a sequence of solutions with unbounded energy. This answers a question of Ambrosetti, Brezis and Cerami. The main ingredient is a new critical point theorem, which guarantees the existence of infinitely many critical values of an even functional in a bounded range. We can also treat strongly indefinite functionals and obtain similar results for firstorder Hamiltonian systems. 
Access type 
: 
Accès restreint 
Publication date 
: 
1995 
Language 
: 
Anglais 
Journal information 
: 
"American Mathematical Society. Proceedings"  Vol. 123, no. 11, p. 35553561 (1995) 
Peer reviewed 
: 
yes 
Publisher 
: 
Amer Mathematical Soc (Providence)

issn 
: 
00029939 
eissn 
: 
10886826 
Publication status 
: 
Publié 
Affiliation 
: 
UCL
 SC/MATH  Département de mathématique

Links 
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