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.
Analysis and Mathematical Physics – Springer Journals
Published: Dec 1, 2021
Keywords: Elliptic Schrödinger system; Monotone iterative method; Control constraint
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