LOW DIMENSIONAL INSTABILITY FOR SEMILINEAR AND QUASILINEAR PROBLEMS IN R-N

作者：Castorina Daniele^*; Esposito Pierpaolo; Sciunzi Berardino

来源：Communications on Pure and Applied Analysis, 2009, 8(6): 1779-1793.

DOI：10.3934/cpaa.2009.8.1779

• p-Laplace operator
• linear instability
• critical dimension

Stability properties for solutions of -Delta(m)(u) = f(u) in R-N are investigated, where N >= 2 and m >= 2. The aim is to identify a cri tic a l dimension N-# so that e very non-constant solutionislinearlyunstable when ever 2 <= N < N-#. For positive, increasing and convex nonlinearities f(u), global bounds on f f ''/(f')(2) allows us to find adimension N-#, which is optimal for exponential and power nonlinearities. In the radial setting we can deal more generally with C-1-nonlinearities and the dimension N-# we find is still optimal.

• 出版日期2009-11