TY - JOUR
T1 - The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity
AU - Ferrero, Alberto
AU - Grunau, Hans Christoph
N1 - Funding Information:
Financial support by the Vigoni programme of CRUI (Rome) and DAAD (Bonn) is gratefully acknowledged. Corresponding author. E-mail address: [email protected] (H.-Ch. Grunau).
PY - 2007/3/15
Y1 - 2007/3/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33846329853&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2006.11.007
DO - 10.1016/j.jde.2006.11.007
M3 - Article
SN - 0022-0396
VL - 234
SP - 582
EP - 606
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -