Singular radial solutions for the Lin-Ni-Takagi equation
| Autor: | Jean-Baptiste Casteras, Juraj Földes |
|---|---|
| Přispěvatelé: | Geometric Analysis and Partial Differential Equations, Department of Mathematics and Statistics |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
ELLIPTIC NEUMANN PROBLEM
NONLINEARITY POSITIVE SOLUTIONS 01 natural sciences Mathematics - Analysis of PDEs Singular solution Neumann boundary condition Classical Analysis and ODEs (math.CA) FOS: Mathematics 111 Mathematics Ball (mathematics) 0101 mathematics Mathematics Applied Mathematics 010102 general mathematics Mathematical analysis LEAST-ENERGY SOLUTIONS Supercritical fluid INTERIOR SEGMENTS 010101 applied mathematics Nonlinear system Mathematics - Classical Analysis and ODEs SPIKES Symmetric solution Exponent 35B32 35B05 35J15 34B40 Analysis Analysis of PDEs (math.AP) |
| Popis: | We study singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension $N\geq 3$. It is shown that for any ball and any $k \geq 0$, there is a singular solution that satisfies Neumann boundary condition and oscillates at least $k$ times 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. 16 pages |
| Databáze: | OpenAIRE |
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