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Search: All articles in the CMB digital archive with keyword Hamiltonian

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1. CMB 2015 (vol 58 pp. 651)

Tang, Xianhua
Ground State Solutions of Nehari-Pankov Type for a Superlinear Hamiltonian Elliptic System on ${\mathbb{R}}^{N}$
This paper is concerned with the following elliptic system of Hamiltonian type \[ \left\{ \begin{array}{ll} -\triangle u+V(x)u=W_{v}(x, u, v), \ \ \ \ x\in {\mathbb{R}}^{N}, \\ -\triangle v+V(x)v=W_{u}(x, u, v), \ \ \ \ x\in {\mathbb{R}}^{N}, \\ u, v\in H^{1}({\mathbb{R}}^{N}), \end{array} \right. \] where the potential $V$ is periodic and $0$ lies in a gap of the spectrum of $-\Delta+V$, $W(x, s, t)$ is periodic in $x$ and superlinear in $s$ and $t$ at infinity. We develop a direct approach to find ground state solutions of Nehari-Pankov type for the above system. Especially, our method is applicable for the case when \[ W(x, u, v)=\sum_{i=1}^{k}\int_{0}^{|\alpha_iu+\beta_iv|}g_i(x, t)t\mathrm{d}t +\sum_{j=1}^{l}\int_{0}^{\sqrt{u^2+2b_juv+a_jv^2}}h_j(x, t)t\mathrm{d}t, \] where $\alpha_i, \beta_i, a_j, b_j\in \mathbb{R}$ with $\alpha_i^2+\beta_i^2\ne 0$ and $a_j\gt b_j^2$, $g_i(x, t)$ and $h_j(x, t)$ are nondecreasing in $t\in \mathbb{R}^{+}$ for every $x\in \mathbb{R}^N$ and $g_i(x, 0)=h_j(x, 0)=0$.

Keywords:Hamiltonian elliptic system, superlinear, ground state solutions of Nehari-Pankov type, strongly indefinite functionals
Categories:35J50, 35J55

2. CMB 2009 (vol 52 pp. 416)

Malik, Shabnam; Qureshi, Ahmad Mahmood; Zamfirescu, Tudor
Hamiltonian Properties of Generalized Halin Graphs
A Halin graph is a graph $H=T\cup C$, where $T$ is a tree with no vertex of degree two, and $C$ is a cycle connecting the end-vertices of $T$ in the cyclic order determined by a plane embedding of $T$. In this paper, we define classes of generalized Halin graphs, called $k$-Halin graphs, and investigate their Hamiltonian properties.

Keywords:$k$-Halin graph, Hamiltonian, Hamiltonian connected, traceable
Categories:05C45, 05C38

3. CMB 2001 (vol 44 pp. 323)

Schuman, Bertrand
Une classe d'hamiltoniens polynomiaux isochrones
Soit $H_0 = \frac{x^2+y^2}{2}$ un hamiltonien isochrone du plan $\Rset^2$. On met en \'evidence une classe d'hamiltoniens isochrones qui sont des perturbations polynomiales de $H_0$. On obtient alors une condition n\'ecessaire d'isochronisme, et un crit\`ere de choix pour les hamiltoniens isochrones. On voit ce r\'esultat comme \'etant une g\'en\'eralisation du caract\`ere isochrone des perturbations hamiltoniennes homog\`enes consid\'er\'ees dans [L], [P], [S]. Let $H_0 = \frac{x^2+y^2}{2}$ be an isochronous Hamiltonian of the plane $\Rset^2$. We obtain a necessary condition for a system to be isochronous. We can think of this result as a generalization of the isochronous behaviour of the homogeneous polynomial perturbation of the Hamiltonian $H_0$ considered in [L], [P], [S].

Keywords:Hamiltonian system, normal forms, resonance, linearization
Categories:34C20, 58F05, 58F22, 58F30

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