F. Gazzola, CRITICAL GROWTH PROBLEMS FOR POLYHARMONIC OPERATORS, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 128, 1998, pp. 251-263
We prove that critical growth problems for polyharmonic operators admi
t nontrivial solutions for a wide class of lower-order perturbations o
f the critical term. The results highlight the phenomenon of bifurcati
on of the critical dimensions discovered by Pucci and Serrin; moreover
, we show that another bifurcation seems to appear for 'nonresonant' d
imensions.