Existence and Concentration of Solutions for the Chern–Simons–Schrödinger System with General Nonlinearity

Tang, Xianhua; Zhang, Jian; Zhang, Wen

doi:10.1007/s00025-016-0553-8

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Cited by 27 publications

(6 citation statements)

References 24 publications

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“…Thus, (19) holds. Finally, (H5) implies that I is an even functional on E, and by Lemma 4 I satisfies all the conditions of Lemma 2.…”

Section: Preliminariesmentioning

confidence: 94%

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

Liu

O’Regan

2021

NAMC

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“…Thus, (19) holds. Finally, (H5) implies that I is an even functional on E, and by Lemma 4 I satisfies all the conditions of Lemma 2.…”

Section: Preliminariesmentioning

confidence: 94%

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

Liu

O’Regan

2021

NAMC

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“…Without (AR) condition, via variational methods, they studied the existence, nonexistence and multiplicity of standing waves for asymptotically linear nonlinearity case. Afterwards, Tang et al [22] assumed the potential V (|x|) satisfies the following conditions:…”

Section: Introductionmentioning

confidence: 99%

Positive ground state solutions for the Chern–Simons–Schrödinger system

Chen

2022

Anal.Math.Phys.

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“…where χ : R 1+2 → R is an arbitrary C ∞ function. Recently, the existence of stationary states for system (1.1) has been extensively investigated, see for example [8,9,10,11,12,17,15,22,23,28,29,32]. In these references, the authors seek the solutions to (1.1) of the following form If we insert the ansatz (1.2) into the system (1.1), then (1.1) is reduced to the following nonlocal elliptic equation:…”

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of normalized solutions for the nonlinear Chern–Simons–Schrödinger equations

Chen¹,

Xie²

2020

Ann. Acad. Sci. Fenn. Math.

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In this paper, we prove the existence and multiplicity results of solutions with prescribed L 2-norm for a class of nonlinear Chern-Simons-Schrödinger equations in R 2 2 −ˆR 2 F (u) constrained on the L 2-spheres S r (c) = u ∈ H 1 r (R 2) : u 2 2 = c. Here, c > 0 and F (s) :=´s 0 f (t) dt. Under some mild assumptions on f , we show that critical points of E κ unbounded from below on S r (c) exist for certain c > 0. In addition, we establish the existence of infinitely many critical points {u κ n } of E κ on S r (c) provided that f is odd. Finally, we regard κ as a parameter and and present a convergence property of u κ n as κ ց 0. These results improve and generalize the existing ones in the literature.

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Existence and Concentration of Solutions for the Chern–Simons–Schrödinger System with General Nonlinearity

Cited by 27 publications

References 24 publications

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

Positive ground state solutions for the Chern–Simons–Schrödinger system

Existence and multiplicity of normalized solutions for the nonlinear Chern–Simons–Schrödinger equations

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