Existence and Nonexistence of Entire Solutions for Non-Cooperative Cubic Elliptic Systems

Hugo Tavares, Susanna Terracini, Gianmaria Verzini, Tobias Weth

Type: Article

Publication Date: 2011-10-14

Citations: 43

DOI: https://doi.org/10.1080/03605302.2011.574244

Abstract

In this article we deal with the cubic Schrödinger system where β = (β i, j ) ij is a symmetric matrix with real coefficients and β ii ≥ 0 for every i = 1,…, n. We analyze the existence and nonexistence of nontrivial solutions in connection with the properties of the matrix β, and provide a complete characterization in dimensions N = 1, 2. Extensions to more general power-type nonlinearities are given.

Locations

Communications in Partial Differential Equations - View
arXiv (Cornell University) - View - PDF

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