In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity the...In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.展开更多
研究了阻尼振动问题{(t)+g(t)(t)=▽F(t,u(t)),a.e.t∈[0,T];u(0)-u(T)=(0)-(T)=0.其中,T>0,g(t)∈L∞(0,T;R),G(t)=integral from n=0 to t g(s)ds,G(T)=0,F:[0,T]×RN→R.给出了其变分原理和2个周期解的存在性定理.即...研究了阻尼振动问题{(t)+g(t)(t)=▽F(t,u(t)),a.e.t∈[0,T];u(0)-u(T)=(0)-(T)=0.其中,T>0,g(t)∈L∞(0,T;R),G(t)=integral from n=0 to t g(s)ds,G(T)=0,F:[0,T]×RN→R.给出了其变分原理和2个周期解的存在性定理.即使在g(t)=0特殊情况下,所得结果也是新的.展开更多
基金Supported by the Youth Foundation of Shangqiu Institute of Technology(No.2018XKQ01)
文摘In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.
文摘研究了阻尼振动问题{(t)+g(t)(t)=▽F(t,u(t)),a.e.t∈[0,T];u(0)-u(T)=(0)-(T)=0.其中,T>0,g(t)∈L∞(0,T;R),G(t)=integral from n=0 to t g(s)ds,G(T)=0,F:[0,T]×RN→R.给出了其变分原理和2个周期解的存在性定理.即使在g(t)=0特殊情况下,所得结果也是新的.
基金Supported by Anhui Provincial Natural Science Foundation(1408085MA02)the Key Foundation of Anhui Education Bureau(KJ2012A019)211 Project of Anhui University(02303303-33030011,J18520207)
