Periodic Solutions of Prescribed Energy for a Class of Symmetric Singular Dynamical Systems  

出　　处：《Acta Mathematica Sinica,English Series》1994年第4期410-414,共5页数学学报（英文版）

基　　金：Partially supported by NNSF of China

摘　　要：We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solution of prescribed energy under suitable assumptions.Our main assumption is related with the strong force condition of Gordon.We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solution of prescribed energy under suitable assumptions.Our main assumption is related with the strong force condition of Gordon.

关 键 词：Periodic Solutions of Prescribed Energy for a Class of Symmetric Singular Dynamical Systems 

分 类 号：O1[理学—数学]