SUBHARMONIC AND MULTIPLE PERIODIC SOLUTIONSFOR HAMILTONIAN SYSTEMS WITHLOCAL PARTIAL SUBLINEAR NONLINEARITY

摘要

The existence of subharmonic and multiple periodic solutions as wellas the minimality of periods are obtained for the nonautonomous Hamiltonian systems = JH'(t,x) with locally and partially sublinear Hamiltonian H; that is, there ex-ist a decomposition R(2N)= A El) B of R~(2N),an ]0, 1[ and two periodic functions L2/1-([0,T]R~+)andb L~2([0, T],R~+) such that |H'(t,uv)I ≤a(t) v|+b(forall (t, u, v) [0, T] x A x B and |v|~(2) /H(t,v+v))→+or — s |v|inB,uniformly in|v|~(2α) u E A for a.e. t in some non empty open subset C of [0,T]. For the resolution we use ananalogy of Egorov's theorem and a generalized saddle point theorem.