Open AccessLow dimensional instability for semilinear and quasilinear problems in $\mathbb{R}^N$
Author(s) -
Daniele Castorina,
Pierpaolo Esposito,
Berardino Sciunzi
Publication year - 2009
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2009.8.1779
Subject(s) - dimension (graph theory) , instability , regular polygon , constant (computer programming) , combinatorics , exponential function , physics , mathematics , stability (learning theory) , mathematical analysis , mathematical physics , quantum mechanics , geometry , computer science , programming language , machine learning
Stability properties for solutions of $-\Delta_m(u)=f(u)$ in $\mathbb{R}^N$ are investigated, where $N\geq 2$ and $m \geq 2$. The aim is to identify a critical dimension $N^\#$ so that every non-constant solution is linearly unstable whenever $2\leq\ud N