Gießen June 16 - 17, 2011
|Nonlinear PDE Days
Frankfurt - Giessen - Karlsruhe
June 16 - 17, 2011
Concentration phenomena in
Thursday, June 16, 2011
2:00 - 2:50 p. m.
"Finite Morse index solutions of nonlinear elliptic PDE's"
Abstract: We discuss finite Morse index solutions on euclidean space or half spaces and their applications to boundet domain problems with smal diffusion and to the behaviour of branches of solutions when the branch becomes large. We also raise a number of open questions.
3:00 - 3:50 p. m.
"Solutions with mixed positive and negative spikes for some singularly perturbed elliptic problems"
4:30 - 5:20 pm
"Sign changing solutions for some nonlinear Schrödinger equation"
Abstract: I will explain some constructions of sign changing solutions for some seminlinear elliptic equation which arises in the study of stationary waves for nonlinear Schrödinger equations. This construction is inspired by similar construction for compact constant mean curvature surfaces in Euclidean space.
Friday, June 17, 2011
9:00 - 9:50 am
"Single and multi peak solutions in degenerate cases"
Abstract: We discuss the existence and location of single and multi peak positive solutions of
- Laplacian u = rf(u) on D
u = 0 on the boundary of D
in the degenerate case where f(0)=f'(0) and r is large. We see differences of peak location from the standard case in the peak location. In addition, we improve the topological arguments to obtain the natural result on the existence of multi peaks.
10:00 - 10:50 am
"On the stability of the Paneitz-Branson equation"
In this talk, I will describe a joint work (with G. Vaira) about the existence of blowing-up solutions for linear perturbations of the Paneitz-Branson equation.
11:30 - 12:20 am
"The role of minimal surfaces in the study of Allen-Cahn equation"
Abstract: I will review some recent results about the existence of entire solutions of the Allen-Cahn equation and their relation with the theory of minimal surfaces and hypersurfaces. In particular, I will focus on the existence of nontrivial stable solutions.