ABSTRACT
This paper is concerned with the following problem: where , and the self-focusing core supp shrinks to a point as . We show that there is a least energy solution corresponding to and then investigate the limiting profile of concentration for as . The results are supplements to the works of [Ackermann and Szulkin. A concentration phenomenon for semilinear elliptic equations. Arch Ration Mech Anal. 2013;207(3):1075–1089; Fang and Wang. Limiting profile of solutions for Schrödinger equations with shrinking self-focusing core. Calc Var Partial Differential Equations. 2020;59(4):Paper No. 129, 18].
Disclosure statement
No potential conflict of interest was reported by the author(s).