On blow-up of positive solutions for a biharmonic equation involving nearly critical exponent

摘要

In this paper a biharmonic problem with Navier boundary condition involving nearly critical growth is considered: #DELTA#_u~2 = u~((n + 4)/(n - 4) - #tau#), u > 0 in #OMEGA# and u = #DELTA#u = 0 on partial deriv#OMEGA#, where #OMEGA# is a bounded smooth convex domain in R~n (n >= 5) and #tau# > 0 is small. We show that any sequence of positive solutions with #tau# -> 0 has to blow up and concentrate at finitely many points in the interior of the domain #OMEGA#. With blow-up argument, we also give the energy a priori estimate of positive solutions.