Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on \(\mathbb R^n\) (Q380169)
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: Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on \(\mathbb R^n\) |
scientific article; zbMATH DE number 6226504
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on \(\mathbb R^n\) |
scientific article; zbMATH DE number 6226504 |
Statements
Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on \(\mathbb R^n\) (English)
0 references
13 November 2013
0 references
biharmonic operator
0 references
extremal functions
0 references
Rellich-Sobolev inequality
0 references
breaking symmetry
0 references
ground state
0 references
radial ground state
0 references
0 references
0 references
0 references
0 references
0 references
Existence of ground states and radial ground states for the problem NEWLINE\[NEWLINE \begin{cases} \triangle^2u + \lambda\;\text{div} \big(|x|^{-2}\bigtriangledown u\big) = |x|^{-\beta} |u|^{q-2}u\\ \int_{\mathbb R^n} |\triangle u|^2 dx < \infty \end{cases} NEWLINE\]NEWLINE are studied. The problem is variational in nature, and is tackled by considering the extremal functions for suitable functional inequalities.
0 references
