Least Energy Solutions of the Schrödinger–Kirchhoff Equation with Linearly Bounded Nonlinearities

Blow up Analysis of Constraint Minimizers for a Class of Elliptic Equations with Bi-nonlocal Terms

“…In particular, we notice that for s, r = 0, p = 2 and β > 0 in (1.6), it is a hot research topic related to the well-known Gross-Pitaevskii functional (see [10,13]), which is derived from physical experimental phenomena of Bose-Einstein condensates. Roughly speaking, when the external potential V (x) in (1.3) behaves like polynomial, logarithmic, ring-shaped, multi-well and periodic, in these papers the authors have established some results of constraint minimizers on the existence, mass concentration behavior and local uniqueness under L 2 -critical state (see [15,16,17,18,19,24,30,39]). In addition, for s = 1, r = 0, β > 0 and V (x) fulfilling suitable choices, (1.6) is regarded as a Kirchhoff type energy functional and there are many works related to studying the existence and limit behavior of constraint minimizers for (1.5) (cf.…”