Elementary variational approach to positive and negative solutions of a nonlinear algebraic system

By using variational methods and elementary analysis, the conditions for the existence of positive and negative solutions to a nonlinear system are given. Furthermore, some examples are offered to explain that the conditions are new and the results are sharp.

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Bibliographic Details
Published in:Advances in difference equations 2017-10, Vol.2017 (1), p.1-13, Article 322
Main Authors: Zhang, Jiao-Ling, Wang, Gen-Qiang
Format: Article
Language:English
Subjects:
Analysis
critical point
Difference and Functional Equations
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
negative solution
nonlinear algebraic system
Nonlinear systems
Ordinary Differential Equations
Partial Differential Equations
positive solution
variational method
Variational methods
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Description
Summary:By using variational methods and elementary analysis, the conditions for the existence of positive and negative solutions to a nonlinear system are given. Furthermore, some examples are offered to explain that the conditions are new and the results are sharp.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-017-1359-z