Mitidieri; A semilinear fourth order elliptic problem with exponential nonlinearity

Abstract. We study a semilinear fourth order elliptic problem with exponential nonlinearity. Motivated by a question raised in [P.-L. Lions, SIAM Rev., 24 (1982), pp. 441–467], we partially extend results known for the corresponding second order problem. Several new difficulties arise and many problems still remain to be solved. We list those of particular interest in the final section