In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous ...In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian systems.We prove that when the positive integers j and k satisfy the certain conditions,there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.展开更多
In this paper, we consider the minimal period estimates for brake orbits of autonomous subquadratic Hamiltonian systems. We prove that if the Hamiltonian function H ∈ C2（R2n,R） is unbounded and not uniformly coerci...In this paper, we consider the minimal period estimates for brake orbits of autonomous subquadratic Hamiltonian systems. We prove that if the Hamiltonian function H ∈ C2（R2n,R） is unbounded and not uniformly coercive, there exists at least one nonconstant T-periodic brake orbit （z, T） with minimal period T or T/2 for every number T 〉 0.展开更多
The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = J▽H(...The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = J▽H(t, z(t)), where H(t, z) =1/2(B(t)z, z) +H(t, z),B(t) is a semipositive symmetric continuous matrix andH is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a_j T-periodic nonconstant brake solution z_j such that z_j and z_(kj) are distinct.展开更多
基金Partially supported by the National Natural Science Foundation of China(11226156)“New Start”Academic Research Projects of Beijing Union University(ZK201218)
基金partially supported by National Natural Science Foundation of China (Grant Nos.11071123,10621101)National Key Basic Research Program (973 Program) of China (Grant No.2011CB808002)
文摘In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian systems.We prove that when the positive integers j and k satisfy the certain conditions,there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.
基金Supported by Beijing Natural Science Foundation(Grant No.1144012)Beijing Talents Found(Grant No.2014000020124G065)
文摘In this paper, we consider the minimal period estimates for brake orbits of autonomous subquadratic Hamiltonian systems. We prove that if the Hamiltonian function H ∈ C2（R2n,R） is unbounded and not uniformly coercive, there exists at least one nonconstant T-periodic brake orbit （z, T） with minimal period T or T/2 for every number T 〉 0.
基金supported by the National Natural Science Foundation of China(Nos.11501030,11226156)the Beijing Natural Science Foundation(No.1144012)
文摘The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = J▽H(t, z(t)), where H(t, z) =1/2(B(t)z, z) +H(t, z),B(t) is a semipositive symmetric continuous matrix andH is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a_j T-periodic nonconstant brake solution z_j such that z_j and z_(kj) are distinct.
