TY - JOUR

T1 - Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations

AU - Cingolani, Silvia

AU - Jeanjean, Louis

AU - Tanaka, Kazunaga

N1 - Publisher Copyright:
© 2016, Springer International Publishing.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations LA,Vħu=f(|u|2)uinRNwhere N≥ 3 , LA,Vħ is the Schrödinger operator with a magnetic field having source in a C1 vector potential A and a scalar continuous (electric) potential V defined by LA,Vħ=-ħ2Δ-2ħiA·∇+|A|2-ħidivA+V(x).Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain Ω ⊂ RN such that (Formula presented.). For ħ> 0 small we prove the existence of at least cupl (K) + 1 geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as ħ→ 0.

AB - We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations LA,Vħu=f(|u|2)uinRNwhere N≥ 3 , LA,Vħ is the Schrödinger operator with a magnetic field having source in a C1 vector potential A and a scalar continuous (electric) potential V defined by LA,Vħ=-ħ2Δ-2ħiA·∇+|A|2-ħidivA+V(x).Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain Ω ⊂ RN such that (Formula presented.). For ħ> 0 small we prove the existence of at least cupl (K) + 1 geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as ħ→ 0.

KW - Complex-valued solutions

KW - Cuplength

KW - Magnetic fields

KW - Nonlinear Schrödinger equations

KW - Semiclassical limit

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U2 - 10.1007/s11784-016-0347-3

DO - 10.1007/s11784-016-0347-3

M3 - Article

AN - SCOPUS:84995414745

VL - 19

SP - 37

EP - 66

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

SN - 1661-7738

IS - 1

ER -