37 research outputs found
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
is a bounded convex domain in with smooth boundary
We study the asymptotic behaviour of the least energy
solutions of this system as We show that the solution remain
bounded for 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