ON THE MULTIPLICITY OF SOLUTIONS FOR NON-LINEAR PERIODIC PROBLEMS WITH THE NON-LINEARITY CROSSING SEVERAL EIGENVALUES

被引:2
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
关键词
NONTRIVIAL SOLUTIONS; P-LAPLACIAN; FUNCTIONALS; EXISTENCE; EQUATIONS;
D O I
10.1017/S0017089509990346
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we consider a non-linear periodic problem driven by the scalar p-Laplacian and with a non-smooth potential. We assume that the multi-valued right-hand-side non-linearity exhibits an asymmetric behaviour at +/-infinity and crosses a finite number of eigenvalues as we move from -infinity to +infinity. Using a variational approach based on the non-smooth critical-point theory, we show that the problem has at least two non-trivial solutions, one of which has constant sign. For the semi-linear (p = 2), smooth problem, using Morse theory, we show that the problem has at least three non-trivial solutions, again one with constant sign.
引用
收藏
页码:271 / 302
页数:32
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