Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 34, pp. 1-20.

Title:  Some remarks on biharmonic elliptic problems
        with positive, increasing and convex nonlinearities

Authors: Elvise Berchio (Univ. di Torino, Italy)
         Filippo Gazzola (Politecnico di Milano, Italy)
 
Abstract: 
 We study the existence of positive solutions for a fourth order
 semilinear elliptic equation under Navier boundary conditions
 with positive, increasing and convex source term. Both bounded
 and unbounded solutions are considered.
 When compared with second order equations, several differences
 and difficulties arise. In order to overcome these difficulties
 new ideas are needed. But still, in some cases we are able to extend
 only partially the well-known results for second order equations.
 The theoretical and numerical study of radial solutions in the ball
 also reveal some new phenomena, not available for second order
 equations. These phenomena suggest a number of intriguing unsolved
 problems, which we quote in the final section.
 
Submitted October 10, 2004. Published March 23, 2005.
Math Subject Classifications: 35J40, 35J60, 35G30.
Key Words: Semilinear biharmonic equations; minimal solutions;
           extremal solutions.