Nonradial positive solutions for a biharmonic critical growth problem

Abstract

We investigate the existence of nonradial positive solutions for a critical semilinear biharmonic problem defined on a unit ball. The solution is obtained as a minimizer of the quotient functional associated to the problem restricted to appropriate subspaces of $H^2\cap H^1_0$ invariant for the action of a subgroup of $O(N)$. By making use of more careful estimates and some new arguments, we extend Serra's result in [41] to the biharmonic case.