Geodesic
Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 35J40, 35J60, 35G30
Keywords: semilinear biharmonic equations, minimal solutions, extremal solutions 
@article{EJDE_2005__2005__a125,
     author = {Berchio,  Elvise and Gazzola,  Filippo},
     title = {Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1129.35349},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a125/}
}
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Berchio,  Elvise; Gazzola,  Filippo. Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a125/