# Solving elliptic Schrödinger systems with control constraints

Solving elliptic Schrödinger systems with control constraints The aim of this paper is to study the non-cooperative elliptic Schrödinger systems arising in Bose–Einstein condensation phenomena and some nonlinear optical materials. The more delicate case of systems of negative potentials is considered. We prove the existence and multiplicity of nontrivial solutions for the above system in space dimensions N≥3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N\ge 3$$\end{document}. Our proofs are based on symmetric mountain pass method, the monotone iterative method, as well as suitable Schrödinger test-function arguments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Solving elliptic Schrödinger systems with control constraints

, Volume 11 (4) – Dec 1, 2021
20 pages

/lp/springer-journals/solving-elliptic-schr-dinger-systems-with-control-constraints-REp0YNJEF7
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-021-00601-5
Publisher site
See Article on Publisher Site

### Abstract

The aim of this paper is to study the non-cooperative elliptic Schrödinger systems arising in Bose–Einstein condensation phenomena and some nonlinear optical materials. The more delicate case of systems of negative potentials is considered. We prove the existence and multiplicity of nontrivial solutions for the above system in space dimensions N≥3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N\ge 3$$\end{document}. Our proofs are based on symmetric mountain pass method, the monotone iterative method, as well as suitable Schrödinger test-function arguments.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Dec 1, 2021

Keywords: Elliptic Schrödinger system; Monotone iterative method; Control constraint