Constraint Minimizers Of Inhomogeneous Mass Subcritical Minimization Problems

This paper considers minimizers of the following inhomogeneous L-2-subcritical energy functionalE(u):= integral(RN) vertical bar del vertical bar(2)dx - 1/p +1 integral(RN) m(x)vertical bar u vertical bar(p+1)dx,under the mass constraint parallel to u parallel to(2)(2) = M. Here, N >= 1, p is an element of(1,1+4/N), M > 0 and the inhomogeneous term m(x) satisfies 0 < m(x) <= 1. Applying the concentration-compactness principle, we prove that this minimization problem admits minimizers for any M is an element of (0, infinity). Further more, we also present a detail analysis on the influence of m(x) on the limit behavior of minimizers as M -> infinity.