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

by Ferrero, Alberto; Grunau, Hans-Christoph


Preprint series: 06-24, Preprints

The paper is published: J. Differ. Equ. 234 (2007), 582-606.

35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
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

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