Zurück zu den Preprints des Jahres 2006


2006-24

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

by Ferrero, Alberto, Grunau, Hans-Christoph.


Series: 2006-24, Preprints

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35J40 Boundary value problems for higher-order elliptic equations

Abstract:
For a semilinear biharmonic Dirichlet problem in the ball with
supercritical power-type nonlinearity,
existence/nonexistence, regularity and stability of radial positive minimal
solutions are studied. 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 in particular a suitable Lyapunov
(energy) function are employed.

Keywords:
supercritical power-type growth, minimal regular solution, asymptotic behaviour

This paper was published in:
J. Differ. Equ. 234 (2007), 582-606.