The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity

Alberto Ferrero, Hans Christoph Grunau

Research output: Contribution to journalArticlepeer-review

Abstract

For a semilinear biharmonic Dirichlet problem in the ball with supercritical power-type nonlinearity, we study existence/nonexistence, regularity and stability of radial positive minimal solutions. Moreover, qualitative properties, and in particular the precise asymptotic behaviour near x = 0 for (possibly existing) singular radial solutions, are deduced. Dynamical systems arguments and a suitable Lyapunov (energy) function are employed.

Original languageEnglish
Pages (from-to)582-606
Number of pages25
JournalJournal of Differential Equations
Volume234
Issue number2
DOIs
Publication statusPublished - 15 Mar 2007
Externally publishedYes

Fingerprint

Dive into the research topics of 'The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity'. Together they form a unique fingerprint.

Cite this