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.
LOW DIMENSIONAL INSTABILITY FOR SEMILINEAR AND QUASILINEAR PROBLEMS IN R-N
SCIUNZI, Berardino
2009-01-01
Abstract
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.File in questo prodotto:
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