Existence And Asymptotic Behavior Of Minimizers For A Constrained Variational Problem

This thesis is concerned with the following constrained variational minimization problem in a special complete subspace H in Wl<p (Rn), where a ≥0 is a parameter andThe existence and asymptotic behavior of minimizers of problem (2) are investigated. Rough-ly speaking, we proved that there exists a*= a*(n,p)> 0, which can be given explicitly, such that the problem(2) has a minimizer if 0< a< a* and has no minimizer if a> a*.Furthermore, we proved that when a (?) a*, the minimizers of problem (2) will blow up at the point x= 0. In addition, we gave accurate characterization of the blow-up rate.