THREE NONTRIVIAL SOLUTIONS FOR NEUMANN PROBLEMS RESONANT AT ANY POSITIVE EIGENVALUE

被引：1
|
作者：
Kyritsi, Sophia Th. [1 ]
Papageorgiou, Nikolaos S. [2 ]
机构：
[1] Hellen Naval Acad, Dept Math, Piraeus 18539, Greece
[2] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece
来源：
MATEMATICHE | 2010年 / 65卷 / 02期
关键词：
Resonance; Concave term; Unique continuation property; Ekeland variational principle; Critical groups; Morse relation; Nondegenerate critical point;
D O I：
10.4418/2010.65.2.10
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider a semilinear Neumann problem with a parametric reaction which has a concave term and a perturbation which at +/-infinity can be resonant with respect to any positive eigenvalue. Using variational methods based on the critical point theory and Morse theory, we show that there exists a critical parameter value lambda* > 0 such that if lambda is an element of (0, lambda*), then the problem has at least three nontrivial smooth solutions.
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页码：79 / 95
页数：17
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