Minimizers of L2-subcritical variational problems with spatially decaying nonlinearities in bounded domains

Abstract

This paper is concerned with the minimizers of L²-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Ω of ℝ^N (N ≥ 1). We prove that the problem admits minimizers for any M > 0. Moreover, the limiting behavior of minimizers as M → ∞ is also analyzed rigorously.