Hamiltonian elliptic systems: a guide to variational frameworks

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...

A Variational Approach to Estimating Uncertain Parameters in Elliptic Systems

A User Guide to Language Frameworks

This user guide explains what language frameworks are and how new language frameworks can be defined. Language frameworks are tools that allow new problem-solving shells to be defined for BB1. They define English-like higher-level languages for describing problem-solving actions, events, and states that are important to solving broad, domain-independent classes of problems. For example, the ACC...

Entire solutions to equivariant elliptic systems with variational structure

In the present paper we consider the system ∆u−Wu(u) = 0, where u : R → R, for a class of potentials W : R → R that possess several global minima and are invariant under a general finite reflection group G. We establish existence of nontrivial entire solutions connecting the global minima of W along certain directions at infinity.

A Variational Principle for Eigenvalue Problems of Hamiltonian Systems

We consider the bifurcation problem u+λu = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue λ. We give a variational characterization of the bifurcating branch λ as a function of the amplitude of the solution. As an application we show how it can be used to obtain simple approximate closed formulae for the period of large amp...