"Non UBC"@en .
"DSpace"@en .
"Gabriele Mancini"@en .
"2019-11-04T09:38:57Z"@en .
"2019-05-07T14:39"@en .
"I will discuss some results obtained in collaboration with Massimo \nGrossi, Angela Pistoia and Daisuke Naimen concerning the existence of \nnodal solutions for the problem\n$$\n-\Delta u = \lambda u e^{u^2+|u|^p} \text{ in }\Omega, u = 0 \text{ on \n}\partial \Omega,\n$$\nwhere $\Omega\subseteq \mathbb R^2$ is a bounded smooth domain and \n$p\to 1^+$.\n If $\Omega$ is ball, it is known that the case $p=1$ defines a \ncritical threshold between the existence and the non-existence of \nradially symmetric sign-changing solutions with $\lambda$ close to $0$. \nIn our work we construct a blowing-up family of nodal solutions to such \nproblem as $p\to 1^+$, when $\Omega$ is an arbitrary domain and \n$\lambda$ is small enough. To our knowledge this is the first \nconstruction of sign-changing solutions for a Moser-Trudinger type \ncritical equation on a non-symmetric domain."@en .
"https://circle.library.ubc.ca/rest/handle/2429/72177?expand=metadata"@en .
"37.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Sapienza Universit\u00E0 di Roma"@en .
"Banff (Alta.)"@en .
"10.14288/1.0384911"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Postdoctoral"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Partial differential equations"@en .
"Differential geometry"@en .
"Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains."@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/72177"@en .