Structure of the positive radial solutions for the supercritical Neumann problem \(\varepsilon^2\Delta u-u+u^p=0\) in a ball (Q2786743)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Structure of the positive radial solutions for the supercritical Neumann problem \(\varepsilon^2\Delta u-u+u^p=0\) in a ball |
scientific article; zbMATH DE number 6544771
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Structure of the positive radial solutions for the supercritical Neumann problem \(\varepsilon^2\Delta u-u+u^p=0\) in a ball |
scientific article; zbMATH DE number 6544771 |
Statements
23 February 2016
0 references
global bifurcation diagram
0 references
intersection number
0 references
singular solution
0 references
Joseph-Lundgren exponent
0 references
math.AP
0 references
Structure of the positive radial solutions for the supercritical Neumann problem \(\varepsilon^2\Delta u-u+u^p=0\) in a ball (English)
0 references
The author investigates the structure of positive radial solutions for the equation NEWLINENEWLINE\[NEWLINE \varepsilon^2\Delta u-u+u^p=0\quad\text{in }B_1(0)\setminus\{0\}\subset{\mathbb R}^N, \quad N\geq 3 NEWLINE\]NEWLINE NEWLINEsubject to homogeneous Neumann boundary conditions, where \(p>(N+2)/(N-2)\). It is shown that there exists a sequence \(\{\varepsilon_n\}\) of positive numbers that converges to zero, for which the above problem has infinitely many singular solutions. Further, asymptotic and bifurcation properties with respect to \(\varepsilon\) are investigated.
0 references
