TY - JOUR
T1 - Multiplicity of Normalized Solutions for the Fractional Schrödinger Equation with Potentials
AU - Zhang, X.
AU - Squassina, Marco
AU - Zhang, J.
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 - https://publicatt.unicatt.it/handle/10807/269616
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85187889548&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85187889548&origin=inward
U2 - 10.3390/math12050772
DO - 10.3390/math12050772
M3 - Article
SN - 2227-7390
VL - 12
SP - 1
EP - 20
JO - Mathematics
JF - Mathematics
IS - 5
ER -