Abstract
We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations (Formula presented.)where (Formula presented.), (Formula presented.) is the Schrödinger operator with a magnetic field having source in a (Formula presented.) vector potential A and a scalar continuous (electric) potential V defined by (Formula presented.)Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain (Formula presented.) such that (Formula presented.)and we set (Formula presented.). For (Formula presented.) small we prove the existence of at least (Formula presented.) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as (Formula presented.).
| Original language | English |
|---|---|
| Pages (from-to) | 1-30 |
| Number of pages | 30 |
| Journal | Journal of Fixed Point Theory and Applications |
| DOIs | |
| Publication status | Accepted/In press - 2016 Nov 14 |
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Keywords
- Complex-valued solutions
- Cuplength
- Magnetic fields
- Nonlinear Schrödinger equations
- Semiclassical limit
ASJC Scopus subject areas
- Modelling and Simulation
- Geometry and Topology
- Applied Mathematics
Cite this
Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations. / Cingolani, Silvia; Jeanjean, Louis; Tanaka, Kazunaga.
In: Journal of Fixed Point Theory and Applications, 14.11.2016, p. 1-30.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations
AU - Cingolani, Silvia
AU - Jeanjean, Louis
AU - Tanaka, Kazunaga
PY - 2016/11/14
Y1 - 2016/11/14
N2 - We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations (Formula presented.)where (Formula presented.), (Formula presented.) is the Schrödinger operator with a magnetic field having source in a (Formula presented.) vector potential A and a scalar continuous (electric) potential V defined by (Formula presented.)Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain (Formula presented.) such that (Formula presented.)and we set (Formula presented.). For (Formula presented.) small we prove the existence of at least (Formula presented.) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as (Formula presented.).
AB - We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations (Formula presented.)where (Formula presented.), (Formula presented.) is the Schrödinger operator with a magnetic field having source in a (Formula presented.) vector potential A and a scalar continuous (electric) potential V defined by (Formula presented.)Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain (Formula presented.) such that (Formula presented.)and we set (Formula presented.). For (Formula presented.) small we prove the existence of at least (Formula presented.) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as (Formula presented.).
KW - Complex-valued solutions
KW - Cuplength
KW - Magnetic fields
KW - Nonlinear Schrödinger equations
KW - Semiclassical limit
UR - http://www.scopus.com/inward/record.url?scp=84995414745&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84995414745&partnerID=8YFLogxK
U2 - 10.1007/s11784-016-0347-3
DO - 10.1007/s11784-016-0347-3
M3 - Article
SP - 1
EP - 30
JO - Journal of Fixed Point Theory and Applications
JF - Journal of Fixed Point Theory and Applications
SN - 1661-7738
ER -