Abstract
This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents (S_{pm varepsilon}): Delta ^{2}u-c_{n}Delta u+d_{n}u = Ku^{ frac{n+4}{n-4}pm varepsilon}, u>0 on S^{n}, where ngeq 5, ε is a small positive parameter and K is a smooth positive function on S^{n}. We construct some solutions of (S_{-varepsilon}) that blow up at one critical point of K. However, we prove also a nonexistence result of single-peaked solutions for the supercritical equation (S_{+varepsilon}).
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