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PreprintarXiv licencearXiv

Multi-peak solutions for a magnetic nonlinear Schrödinger equation with exponential critical growth in ℝ2

  • Pietro d'Avenia
  • Chao Ji
  • Qingyue Li
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Abstract

In this paper, we study the following magnetic nonlinear Schrödinger equation (ε/i∇−A(x))2u+V(x)u=f(|u|2)u in ℝ2, where ε>0 is a parameter, A∈ C(ℝ2, ℝ2) is a magnetic potential, V∈ C(ℝ2, ℝ) is a multi-well potential, and f∈ C1(ℝ, ℝ) exhibits exponential critical growth. By variational methods and a penalization technique, we prove the existence and multiplicity of nontrivial solutions for sufficiently small ε>0. If, in addition, A∈ C1(ℝ2,ℝ2), we show that these solutions have multiple peaks and we establish their concentration behavior and exponential decay.

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Cite

BibTeXRIS
BibTeX
@misc{davenia2026multipeak,
  title = {{Multi-peak solutions for a magnetic nonlinear Schrödinger equation with exponential critical growth in $\mathbbR^2$}},
  author = {Pietro d'Avenia and Chao Ji and Qingyue Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17250},
  eprint = {2610.17250},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17250},
}
RIS
TY  - UNPB
TI  - Multi-peak solutions for a magnetic nonlinear Schrödinger equation with exponential critical growth in ℝ^2
AU  - Pietro d'Avenia
AU  - Chao Ji
AU  - Qingyue Li
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17250
UR  - https://arxiv.org/abs/2610.17250
AB  - In this paper, we study the following magnetic nonlinear Schrödinger equation (ε/i∇−A(x))^2u+V(x)u=f(|u|^2)u in ℝ^2, where ε>0 is a parameter, A∈ C(ℝ^2, ℝ^2) is a magnetic potential, V∈ C(ℝ^2, ℝ) is a multi-well potential, and f∈ C^1(ℝ, ℝ) exhibits exponential critical growth. By variational methods and a penalization technique, we prove the existence and multiplicity of nontrivial solutions for sufficiently small ε>0. If, in addition, A∈ C^1(ℝ^2,ℝ^2), we show that these solutions have multiple peaks and we establish their concentration behavior and exponential decay.
ER  -