Multiplicity of Periodic Bouncing Solutions for Sublinear Damped Variation Systems via Nonsmooth Variational Methods  

作　　者：Si Qi WANG Fei GUO 

机构地区：[1]School of Mathematics,Tianjin University,Tianjin 300354,China [2]Tianjin Key Laboratory of Brain-Inspired Intelligence Technology,Tianjin 300354,China

出　　处：《Acta Mathematica Sinica,English Series》2023年第7期1332-1350,共19页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 12171355);Elite Scholar Program in Tianjin University,P. R. China。

摘　　要：Two results about the multiplicity of nontrivial periodic bouncing solutions for sublinear damped vibration systems-x=g(t)x+f(t,x) are obtained via the Generalized Nonsmooth Saddle Point Theorem and a technique established by Wu Xian and Wang Shaomin.Both of them imply the condition "f≥0" required in some previous papers can be weakened,furthermore,one of them also implies the condition about ■F(t,x)/■t required in some previous papers,such as "|■F(t,x)/■t|=σ_(0)F(t,x)" and "|■F(t,x)/■t|≤C(1+F(t,x))", is unnecessary,where F(t,x):=∫_(0)~xf(t,x)ds,and σ_(0),C are positive constants.

关 键 词：Damped vibration systems generalized Nonsmooth Saddle Point Theorem sublinear conditions periodic bouncing solutions MULTIPLICITY 

分 类 号：O241.6[理学—计算数学]