Calculus of Variations and Geometric Measure Theory
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E. Berchio - F. Gazzola

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

created on 14 Jun 2004
modified by gazzola on 30 May 2005


Published Paper

Inserted: 14 jun 2004
Last Updated: 30 may 2005

Year: 2004


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 the second order equations. These phenomena suggest a number of intriguing unsolved problems, which we quote in the final section.


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