Critical gauged Schr\"{o}dinger equations in R^2 with vanishing potentials

Liejun Shen; Marco Squassina; Minbo Yang

Critical gauged Schr\"{o}dinger equations in R^2 with vanishing potentials

Analysis of PDEs 2022-03-25 v2

Authors: Liejun Shen , Marco Squassina , Minbo Yang

Abstract

We study a class of gauged nonlinear Schr\"{o}dinger equations in the plane. We obtain existence of two nontrivial solutions via the Mountain-Pass theorem and Ekeland's variational principle. Moreover, we prove existence of infinitely many solutions for odd nonlinearities.

Keywords

gauged schrödinger equations vanishing potentials mountain-pass theorem ekeland variational principle nontrivial solutions odd nonlinearities

Cite

@article{arxiv.2110.14260,
  title  = {Critical gauged Schr\"{o}dinger equations in R^2 with vanishing potentials},
  author = {Liejun Shen and Marco Squassina and Minbo Yang},
  journal= {arXiv preprint arXiv:2110.14260},
  year   = {2022}
}

Comments

22 pages, minor revision, accepted in DCDS-A

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