Closed characteristics on non-compact hypersurfaces in R^2n.

Viterbo demonstrated that any (2n - 1)-dimensional compact hypersurface M ⊂

Asymptotic behaviour of a semilinear elliptic system with a large exponent

Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quad v>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad \Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where $\Omega$ is a bounded convex domain in $\R^N,$ $N>2,$ with smooth boundary $\partial \Omega.$ We study the asymptotic behaviour of the least energy solutions of this system as $p\to \infty.$ We show that the solution remain bounded for $p$ large and have one or two peaks away form the boundary. When one peak occurs we characterize its location.Comment: 16 pages, submmited for publicatio

Scalar parabolic PDE's and braids

The comparison principle for scalar second order parabolic PDEs on functions u(t, x) admits a topological interpretation: pairs of solutions,

Differential systems with strongly indefinite variational structure

AbstractThe Euler-Lagrange equations of Lagrangians with a strongly indefinite quadratic part are studied by means of the direct min-max method of Benci and Rabinowitz. The simplest case is a system of two coupled semilinear Poisson equations. Using an analytic framework of a suitable family of products of fractional Sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates