TITLE:
Normalized Ground State Solutions to Fractional Schrödinger Equations with General Nonlinearities
AUTHORS:
Yifei Zhang
KEYWORDS:
Fractional Schrödinger Equation, Normalized Solution, Constrained Minimization
JOURNAL NAME:
Open Access Library Journal,
Vol.12 No.4,
April
29,
2025
ABSTRACT: This paper investigates the existence of normalized solutions to a fractional Schrödinger equation with combined nonlinearities. In previous studies, the equation
−Δu+λu=g(
u
)+
| u |
q−2
u
. where
N≥3,2<q<
2
*
=
2N
N−2
has been proven to have solutions through various constraints and methods. Furthermore, we consider the existence of solutions for fractional equations. In the
L
2
-supercritical cases, we employ the Sobolev subcritical approximation method to establish the existence of normalized ground-state solutions.