TY - JOUR

T1 - Multiplicity of Normalized Solutions for the Fractional Schrödinger Equation with Potentials

AU - Zhang, Xue

AU - Squassina, Marco

AU - Zhang, Jianjun

PY - 2024

Y1 - 2024

N2 - We are concerned with the existence and multiplicity of normalized solutions to the fractional Schrödinger equation (Formula presented.), where (Formula presented.) is the fractional Laplacian, (Formula presented.), (Formula presented.), (Formula presented.) is an unknown parameter that appears as a Lagrange multiplier, (Formula presented.) are bounded and continuous, and f is (Formula presented.) -subcritical. Under some assumptions on the potential V, we show the existence of normalized solutions depends on the global maximum points of h when (Formula presented.) is small enough.

AB - We are concerned with the existence and multiplicity of normalized solutions to the fractional Schrödinger equation (Formula presented.), where (Formula presented.) is the fractional Laplacian, (Formula presented.), (Formula presented.), (Formula presented.) is an unknown parameter that appears as a Lagrange multiplier, (Formula presented.) are bounded and continuous, and f is (Formula presented.) -subcritical. Under some assumptions on the potential V, we show the existence of normalized solutions depends on the global maximum points of h when (Formula presented.) is small enough.

KW - fractional Laplacian

KW - mass critical exponent

KW - normalized solution

KW - fractional Laplacian

KW - mass critical exponent

KW - normalized solution

UR - http://hdl.handle.net/10807/269616

U2 - 10.3390/math12050772

DO - 10.3390/math12050772

M3 - Article

SN - 2227-7390

VL - 12

SP - 1

EP - 20

JO - Mathematics

JF - Mathematics

ER -