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2002-35

A semilinear fourth order elliptic problem with exponential nonlinearity

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).