Singular radial solutions for the Lin-Ni-Takagi equation

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http://hdl.handle.net/10138/321645

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Casteras , J-B & Földes , J 2020 , ' Singular radial solutions for the Lin-Ni-Takagi equation ' , Calculus of Variations and Partial Differential Equations , vol. 59 , no. 5 , 168 . https://doi.org/10.1007/s00526-020-01824-3

Title: Singular radial solutions for the Lin-Ni-Takagi equation
Author: Casteras, Jean-Baptiste; Földes, Juraj
Contributor: University of Helsinki, Geometric Analysis and Partial Differential Equations
Date: 2020-09-13
Language: eng
Number of pages: 20
Belongs to series: Calculus of Variations and Partial Differential Equations
ISSN: 0944-2669
URI: http://hdl.handle.net/10138/321645
Abstract: We study singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension N >= 3. It is shown that for any ball and any k >= 0, there is a singular solution that satisfies Neumann boundary condition and oscillates at leastktimes around the constant equilibrium. Moreover, we show that the Morse index of the singular solution is finite or infinite if the exponent is respectively larger or smaller than the Joseph-Lundgren exponent.
Subject: ELLIPTIC NEUMANN PROBLEM
LEAST-ENERGY SOLUTIONS
POSITIVE SOLUTIONS
INTERIOR
NONLINEARITY
SEGMENTS
SPIKES
111 Mathematics
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