Using the calculus of variations in the large,especially computing the category of the symmetric configuration space of symmetric N-body-type problems,we prove the existence of infinitely many symmetric noncollision p...Using the calculus of variations in the large,especially computing the category of the symmetric configuration space of symmetric N-body-type problems,we prove the existence of infinitely many symmetric noncollision periodic solutions about the symmetric and nonau- tonomous N-body-type problems under the assumptions that the symmetric potentials satisfy the strong force condition of Gordon.展开更多
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 solutio...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.展开更多
基金The second author is partially supported by NSFC Grant 19141002 and a FEYUT of SEDC of China.
文摘Using the calculus of variations in the large,especially computing the category of the symmetric configuration space of symmetric N-body-type problems,we prove the existence of infinitely many symmetric noncollision periodic solutions about the symmetric and nonau- tonomous N-body-type problems under the assumptions that the symmetric potentials satisfy the strong force condition of Gordon.
文摘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.
