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

Oswald, P.

Commentat. Math. Univ. Carol. 26, 565-577 (1985).

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

MSC:

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)

Keywords:

positive radial symmetric; homogeneous Dirichlet problem; semilinear biharmonic equation; a priori; existence