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We consider the problem Δ 2 u = K(y)|u| 8/(n-4) u in ℝ n with u, Δu → 0 as |y| → ∞, where K is a bounded and continuous function on ℝ n , n ≥ 5. Our aim is to construct infinitely many solutions which concentrate around k points, k ≥ 2, under some appropriate conditions on K. Moreover we prove that there is no solution which concentrates at one point.

Concentration phenomena for a fourth-order equation on ℝn

Concentration phenomena for a fourth-order equation on ℝⁿ