Abstract
We consider nonlinear Schrödinger equation with time dependent coefficients. Fanelli [5] found a transformation between solutions of the original equation and of the usual Schrödinger equation with power nonlinearity involving time dependent coefficients in some Lorentz spaces. In this paper we extend the results in [5] in space-time integrability properties of solutions. Particularly, we prove that the existence and uniqueness of solutions can be described exclusively in terms of Lebesgue spaces (not Lorentz spaces as in [5]) as far as the space integrability of solutions. We also discuss the equation with coefficient of an explicit homogeneous function and describe the associated Strichartz estimate and contraction mapping argument. Copyright
| Original language | English |
|---|---|
| Pages (from-to) | 1986-2001 |
| Number of pages | 16 |
| Journal | Mathematische Nachrichten |
| Volume | 287 |
| Issue number | 17-18 |
| DOIs | |
| Publication status | Published - 2014 Dec 1 |
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Keywords
- Lorentz space
- Nonlinear Schrödinger equation
- Time dependent coefficient
ASJC Scopus subject areas
- Mathematics(all)
Cite this
On the semilinear Schrödinger equation with time dependent coefficients. / Gonda, Takuya; Machihara, Shuji; Ozawa, Tohru.
In: Mathematische Nachrichten, Vol. 287, No. 17-18, 01.12.2014, p. 1986-2001.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the semilinear Schrödinger equation with time dependent coefficients
AU - Gonda, Takuya
AU - Machihara, Shuji
AU - Ozawa, Tohru
PY - 2014/12/1
Y1 - 2014/12/1
N2 - We consider nonlinear Schrödinger equation with time dependent coefficients. Fanelli [5] found a transformation between solutions of the original equation and of the usual Schrödinger equation with power nonlinearity involving time dependent coefficients in some Lorentz spaces. In this paper we extend the results in [5] in space-time integrability properties of solutions. Particularly, we prove that the existence and uniqueness of solutions can be described exclusively in terms of Lebesgue spaces (not Lorentz spaces as in [5]) as far as the space integrability of solutions. We also discuss the equation with coefficient of an explicit homogeneous function and describe the associated Strichartz estimate and contraction mapping argument. Copyright
AB - We consider nonlinear Schrödinger equation with time dependent coefficients. Fanelli [5] found a transformation between solutions of the original equation and of the usual Schrödinger equation with power nonlinearity involving time dependent coefficients in some Lorentz spaces. In this paper we extend the results in [5] in space-time integrability properties of solutions. Particularly, we prove that the existence and uniqueness of solutions can be described exclusively in terms of Lebesgue spaces (not Lorentz spaces as in [5]) as far as the space integrability of solutions. We also discuss the equation with coefficient of an explicit homogeneous function and describe the associated Strichartz estimate and contraction mapping argument. Copyright
KW - Lorentz space
KW - Nonlinear Schrödinger equation
KW - Time dependent coefficient
UR - http://www.scopus.com/inward/record.url?scp=84913582680&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84913582680&partnerID=8YFLogxK
U2 - 10.1002/mana.201200108
DO - 10.1002/mana.201200108
M3 - Article
AN - SCOPUS:84913582680
VL - 287
SP - 1986
EP - 2001
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 17-18
ER -