"Non UBC"@en . "DSpace"@en . "De Marchis, Francesca"@en . "2018-10-03T22:35:22Z"@* . "2018-04-05T11:16"@en . "We consider the classical Lane Emden equation in bounded domains of the plane with Dirichlet boundary conditions and we present some results concerning the Morse index of solutions to this problem, when the exponent of the nonlinearity is large. Via these Morse index computations and a precise asymptotic analysis we can deduce a uniqueness result for positive solutions in convex domains and also some existence results of non-radial sign-changing solutions in the ball.\nBased on joint papers with M. Grossi, I. Ianni and F. Pacella."@en . "https://circle.library.ubc.ca/rest/handle/2429/67323?expand=metadata"@en . "50 minutes"@en . "video/mp4"@en . ""@en . "Author affiliation: Sapienza Universit\u00E0 di Roma"@en . "10.14288/1.0372386"@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 . "Faculty"@en . "BIRS Workshop Lecture Videos (Banff, Alta)"@en . "Mathematics"@en . "Partial differential equations"@en . "Global analysis, analysis on manifolds"@en . "Uniqueness and existence results via Morse index for Lane Emden problems"@en . "Moving Image"@en . "http://hdl.handle.net/2429/67323"@en .