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. © 2006 Elsevier Inc. All rights reserved.
Ferrero, A., Grunau, H. (2007). The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity. JOURNAL OF DIFFERENTIAL EQUATIONS, 234, 582-606 [10.1016/j.jde.2006.11.007].
The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity
FERRERO, ALBERTO;
2007
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. © 2006 Elsevier Inc. All rights reserved.
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