A semilinear fourth order elliptic problem with exponential nonlinearity

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


Preprint series: 02-35, Preprints

The paper is published: SIAM J. Math. Anal. 36 , 1226-1258 (2005).

35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
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

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