On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball. (English) Zbl 0612.35055

This work deals with positive radial symmetric solutions of the homogeneous Dirichlet problem for a semilinear biharmonic equation \[ \Delta^ 2u=g(u)\quad in\quad \Omega,\quad u=\partial u/\partial n=0\quad at\quad \partial \Omega, \] where \(\Omega\) is the unit ball. Some a priori \(L^{\infty}\) estimates are established and then existence theorems are proved.
Reviewer: G.Gudmundsdottir


35J65 Nonlinear boundary value problems for linear elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35B45 A priori estimates in context of PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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