Low dimensional instability for semilinear and quasilinear problems in $\mathbb{R}^N$ | Zendy

Daniele Castorina | Zendy; Pierpaolo Esposito | Zendy; Berardino Sciunzi | Zendy

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Low 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 andamp 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

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