SOLUTIONS AND MULTIPLE SOLUTIONS FOR SECOND ORDER PERIODIC SYSTEMS WITH A NONSMOOTH POTENTIAL

被引：0

作者：

Barletta, Giuseppina ^{[1
]}

Papageorgiou, Nikolaos S. ^{[2
]}

机构：

[1] Univ Reggio Calabria, Dipartimento Patrimonio Architetton & Urbanist, I-89124 Reggio Di Calabria, Italy

[2] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2013年 / 43卷 / 04期

关键词：

Locally Lipschitz potential; generalized subdifferential; PSc-condition; second deformation theorem; linking sets; multiple nontrivial solutions; HAMILTONIAN-SYSTEMS;

D O I：

10.1216/RMJ-2013-43-4-1059

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A nonautonomous second order system with a nonsmooth potential is studied. Using the nonsmooth critical point theory, first an existence theorem is proved. Then, by strengthening the hypotheses on the nonsmooth potential, a multiplicity theorem is proved using the nonsmooth second deformation. The hypotheses on the nonsmooth potential make the Euler functional of the problem bounded below but do not make it coercive. Moreover, the analytical framework of the paper incorporates strongly resonant periodic systems.

引用

页码：1059 / 1075

页数：17

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