Subharmonics of a Nonconvex Noncoercive Hamiltonian System

Subharmonic solutions of a nonconvex noncoercive Hamiltonian system

In this paper we study the existence of subharmonic solutions of the Hamiltonian system Jẋ + u∗∇G(t, u(x)) = e(t) where u is a linear map, G is a C-function and e is a continuous function.

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Existence of Minimizers for Nonconvex, Noncoercive Simple Integrals

We consider the problem of minimizing autonomous, simple integrals like

Subharmonics with Minimal Periods for Convex Discrete Hamiltonian Systems

and Applied Analysis 3 Lemma 6 (see [12, proposition 2.2]). LetH : R → R be of C 1 and convex functional, −β ≤ H(u) ≤ αq|u| + γ, where u ∈ R, α > 0, q > 1, β ≥ 0, γ ≥ 0. Then αp|∇H(u)| ≤ (∇H(u), u) + β + γ, where 1/p + 1/q = 1. In order to know the form of u ∈ E pT , we consider eigenvalue problem LJΔu (n − 1) = λu (n) , u (n + pT) = u (n) , (12) where u(n) = ( u1(n) u2(n) ), Lu(n − 1) = ( u1(n...

An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...