Critical semilinear biharmonic equations in R^N

Abstract

Synopsis An existence theorem is obtained for a fourth-order semilinear elliptic problem in R N involving the critical Sobolev exponent (N + 4)/(N − 4), N>4. A preliminary result is that the best constant in the Sobolev embedding L 2N/(N–4) (R N ) is attained by all translations and dilations of (1 + ∣x∣ 2 ) (4-N)/2 . The best constant is found to be