| This dissertation, which expands the result in paper [6], is devoted to studying the following variational problemswhere p~* = (?) is Sobolev exponent, N＞p＞1,N≥3, at the same time with 0≤F(t)≤(?) . It consists of two chapters.In the first chaper, introducing some famous theorems, we prove local generalized Sobolev inequality and a generalized concentration-compactnesstheorem.Chaper 2 obtains that asε→0, the almost extremals of the above variational problem concentrate at a single point, and the local behaviourof the almost extremals near the concentration point only depends on F. Moreover, we find that the almost extremal sequence tend to an extremal for the generalied Sobolev constant on R~N providedthat F satifies certain growth conditions at 0 and infinity. |
