Existence of Solutions for a Nonlinear Algebraic System

Guang Zhang and Liang Bai

Discrete Dynamics in Nature and Society, 2009, vol. 2009, 1-28

Abstract:

As well known, the existence and nonexistence of solutions for nonlinear algebraic systems are very important since they can provide the necessary information on limiting behaviors of many dynamic systems, such as the discrete reaction-diffusion equations, the coupled map lattices, the compartmental systems, the strongly damped lattice systems, the complex dynamical networks, the discrete-time recurrent neural networks, and the discrete Turing models. In this paper, both the existence of nonzero solution pairs and the nonexistence of nontrivial or nonzero solutions for a nonlinear algebraic system will be considered by using the critical point theory and Lusternik-Schnirelmann category theory. The process of proofs on the obtained results is simple, the conditions of theorems are also easy to be verified, however, some of them improve the known ones even if the system is reduced to the precial cases, in particular, others of them are still new.

Date: 2009
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2009/785068.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2009/785068.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:785068

DOI: 10.1155/2009/785068

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().