by Arioli, G., Gazzola, F., Grunau, H.-Ch., Mitidieri, E..

**Series:** 2002-35, Preprints

- MSC:
- 35J65 Nonlinear boundary value problems for linear elliptic equations
- 35J40 Boundary value problems for higher-order elliptic equations

**Abstract:**

We study a semilinear fourth order elliptic problem

with exponential nonlinearity. Motivated by a question raised by P.L. Lions,

we partially extend known results for the corresponding second order

problem. Several new difficulties arise and many problems still remain to

be solved. We list the ones we feel particularly interesting in the final

section.

**Keywords:**

biharmonic, supercritical growth, exponential nonlinearity, singular solution, regular solution

**This paper was published in:**

SIAM J. Math. Anal. 36 , 1226-1258 (2005).