Positive solutions in semilinear critical problems for polyharmonic operators

In this work, we study the existence of positive solutions in semilinear critical problems for polyharmonic operators. Minimizing on some infinite-dimensional Finsler manifold, we prove the existence result in some general domain under the appropriate assumptions. Alternatively, the concentration phenomenon occurs if minimizing method does not work. This permits us to search for the instable solutions in higher level set by topological arguments in domains perforated with the small holes. (C) 2004 Elsevier SAS. All rights reserved.