Seminario di Equazioni differenziali e applicazioni: “On the global bifurcation diagram of the Gel'fand problem”

Lunedì 15 Aprile 2019, ore 12:30 - Aula 1BC45 - Daniele Bartolucci


Lunedì 15 Aprile 2019 alle ore 12:30 in Aula 1BC45, Daniele Bartolucci (Universià di Roma Tor Vergata) terrà un seminario dal titolo “On the global bifurcation diagram of the Gel'fand problem”.

For a large class of domains $\Omega \subset \mathbb{R}^2$ (which need not be neither simply connected nor symmetric) we describe the qualitative behavior of the global bifurcation diagram of the unbounded branch of solutions crossing the origin $(\mu, v) = (0, 0) \in \mathbb{R} \times C_0^2 (\bar{\Omega})$ of the Gel'fand problem, $$\begin{cases} -\Delta v = \mu e^v \ \textrm{in} \ \Omega \\ v = 0 \ \textrm{on} \ \partial\Omega \end{cases}$$
After an introduction to some well known results, we will describe the main ideas behind the proof. At
least to our knowledge this is the first result about the exact monotonicity of the branch of non-minimal solutions which is not just concerned with radial solutions and/or with symmetric domains. This is part of a joint research project in collaboration with A. Jevnikar.

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