Limit-point criteria for semi-degenerate singular Hamiltonian differential systems with perturbation terms

Billiards: a singular perturbation limit of smooth Hamiltonian flows.

Nonlinear multi-dimensional Hamiltonian systems that are not near integrable typically have mixed phase space and a plethora of instabilities. Hence, it is difficult to analyze them, to visualize them, or even to interpret their numerical simulations. We survey an emerging methodology for analyzing a class of such systems: Hamiltonians with steep potentials that limit to billiards.

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...

Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems

The linearizability or isochronicity problem is one of the open problems for polynomial differential systems which is far to be solved in general. A progressive way to find necessary conditions for linearizability is to compute period constants. In this paper, we are interested in the linearizability problem of p :−q resonant degenerate singular point for polynomial differential systems. Firstl...

Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

Singular Sturmian theory for linear Hamiltonian differential systems

We establish a Sturmian type theorem comparing the number of focal points of any conjoined basis of a nonoscillatory linear Hamiltonian differential system with the number of focal points of the principal solution. We also present various extensions of this statement.