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

作     者：Si Qi WANG Fei GUO Si Qi WANG;Fei GUO

作者机构：School of MathematicsTianjin UniversityTianjin 300354China Tianjin Key Laboratory of Brain-Inspired Intelligence TechnologyTianjin 300354China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第7期

页      面：1332-1350页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

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

主　　题：Damped vibration systems generalized Nonsmooth Saddle Point Theorem sublinear conditions periodic bouncing solutions multiplicity 

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.