TY - ELEC
AU - Gabriele Mancini
PY - 2019
TI - Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains.
LA - eng
M3 - Moving Image
AB - I will discuss some results obtained in collaboration with Massimo
Grossi, Angela Pistoia and Daisuke Naimen concerning the existence of
nodal solutions for the problem
$$
-\Delta u = \lambda u e^{u^2+|u|^p} \text{ in }\Omega, u = 0 \text{ on
}\partial \Omega,
$$
where $\Omega\subseteq \mathbb R^2$ is a bounded smooth domain and
$p\to 1^+$.
If $\Omega$ is ball, it is known that the case $p=1$ defines a
critical threshold between the existence and the non-existence of
radially symmetric sign-changing solutions with $\lambda$ close to $0$.
In our work we construct a blowing-up family of nodal solutions to such
problem as $p\to 1^+$, when $\Omega$ is an arbitrary domain and
$\lambda$ is small enough. To our knowledge this is the first
construction of sign-changing solutions for a Moser-Trudinger type
critical equation on a non-symmetric domain.
N2 - I will discuss some results obtained in collaboration with Massimo
Grossi, Angela Pistoia and Daisuke Naimen concerning the existence of
nodal solutions for the problem
$$
-\Delta u = \lambda u e^{u^2+|u|^p} \text{ in }\Omega, u = 0 \text{ on
}\partial \Omega,
$$
where $\Omega\subseteq \mathbb R^2$ is a bounded smooth domain and
$p\to 1^+$.
If $\Omega$ is ball, it is known that the case $p=1$ defines a
critical threshold between the existence and the non-existence of
radially symmetric sign-changing solutions with $\lambda$ close to $0$.
In our work we construct a blowing-up family of nodal solutions to such
problem as $p\to 1^+$, when $\Omega$ is an arbitrary domain and
$\lambda$ is small enough. To our knowledge this is the first
construction of sign-changing solutions for a Moser-Trudinger type
critical equation on a non-symmetric domain.
UR - https://open.library.ubc.ca/collections/48630/items/1.0384911
ER - End of Reference