New periodic solutions of singular Hamiltonian systems with fixed energies

MULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.  

Periodic Solutions of Second Order Hamiltonian Systems

We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′ x (t, x) , where ε is a small parameter, x ∈ R and V (t, x) is 2π-periodic in t. Moreover we provide two applications.

Periodic solutions of even Hamiltonian systems onthe

We consider the Hamiltonian system (HS) ?J _ z = H z (t; z) where H 2 C 2 (R R 2N ; R) is 2-periodic in all variables, so (HS) induces a Hamiltonian system on the torus T 2N. In addition we assume that H is even in the z-variable. This implies the existence of 2 2N trivial stationary solutions of (HS). We are interested in the existence of nontrivial periodic solutions. Observe that the Arnol'd...

New conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

Periodic Solutions of Spatially Periodic, Even Hamiltonian Systems