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 establ...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.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 12171355)Elite Scholar Program in Tianjin University,P. R. China。
文摘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.
