Brake subharmonic solutions of subquadratic Hamiltonian systems

Li, Chong
May 2016
Chinese Annals of Mathematics;May2016, Vol. 37 Issue 3, p405
Academic Journal
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 ż( t) = J∇H( t, z( t)), where $$H(t,z) = \tfrac{1} {2}(\hat B(t)z,z) + \hat H(t,z),\hat B(t)$$, is a semipositive symmetric continuous matrix and Ĥ is unbounded and not uniformly coercive. It is proved 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.


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