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4 Timoumi M.

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Subharmonic and multiple periodic solutions for Hamiltonian systems with local partial sublinear nonlinearity

Timoumi M.

Demonstratio Mathematica

2009

Vol. 42, nr 2

351-370

The existence of subharmonic and multiple periodic solutions as well as the minimality of periods are obtained for the nonautonomous Hamiltonian systems [...]. For the resolution we use an analogy of Egorov's theorem and a generalized saddle point theorem.

Subharmonic of not uniformly partially coercive Hamiltonian systems

Timoumi M.

Demonstratio Mathematica

2008

Vol. 41, nr 1

233-248

In this work, we prove the existence of multiple periodic and subharmonic solutions of the Hamiltonian system [..] when the Hamiltonian H is periodic in a part of the variables and locally coercive in the other part; that is, there exists a decomposition [...] for almost every t in some non empty open subset C of [O, T]. For the resolution, we use an analogy of Egorov's Theorem and a Generalized Saddle Point Theorem.

Periodic solutions for noncoercive superquadratic Hamiltonian systems

Timoumi M.

Demonstratio Mathematica

2007

Vol. 40, nr 2

331-346

In this note, we study the existence of periodic solutions for the noncoer- cive Hamiltonian system J ˙ x - u*A(t)u(x) + u*G'(t, u(x)) = 0, where the function G satisfies a new superquadratic condition which includes the case G(t, y) = |y|2(ln(1+|y|p))q, p, q > 1. By using a linking theorem, we obtain some new results.

Subharmonics of a Hamiltonian systems class

Timoumi M.

Demonstratio Mathematica

2004

Vol. 37, nr 4

977--990

In this note we are interested in the existence of subharmonics of Hamiltonian system x = JH'(t,x), where H is a convex noncoercive Hamiltonian. This type of Hamiltonian systems governs the motion of relativistic particles. The resolution method consists in finding critical points of dual action integral.