POSITIVE SOLUTIONS OF SINGULAR ALGEBRAIC SYSTEMS WITH A PARAMETER

TitlePOSITIVE SOLUTIONS OF SINGULAR ALGEBRAIC SYSTEMS WITH A PARAMETER
Publication TypeJournal Article
Year of Publication2015
AuthorsLIAN, HAIRONG, WANG, HAIYAN, WU, MENGNIEN, GAO, TANGAN
Volume19
Issue4
Start Page565
Pagination13
Date Published2015
ISSN1083-2564
AMS39A10, 65H10
Abstract

In this paper, we study positive solutions of singular systems of nonlinear algebraic equations with a parameter. With singularity at the origin, superlinearity or sublinearity at infinity, the existence and multiplicity of positive solutions are established. The proof of the results is based on Krasnoselskii fixed point theorem. Some examples are gave to illusive the results.
URLhttp://www.acadsol.eu/en/articles/19/4/8.pdf
Refereed DesignationRefereed
Full Text

REFERENCES
[1] T. Gao, H. Wang, and M. Wu, Nonnegative solutions of a class of systems of algebraic equations,
Dynam. Systems Appl. Accepted for publication.
[2] D. Guo and V. Lakshmikantham, Nonlinear Problem in Abstract Cones, Academic Press,
Orlando, 1988.
[3] M. Krasnoselskii, Positive Solution of Operator Equations, Noordhoff, Groningen, 1964.
[4] H. Wang, Positive periodic solutions of singular systems with a parameter, J. Differential
Equations 249 (2012), 2986–3002.
[5] H. Wang, Positive periodic solutions of singular systems of first order ordinary differential
equations, Appl. Math. Comput., 218 (2011), 1605–1610.
[6] H. Wang, M. Wang and E. Wang, An application of the Krasnoselskii theorem to systems of
algebraic equations, J. Appl. Math. Comput., 38 (2012), 585–600.
[7] Y. Yang and J. Zhang, Existence results for a nonlinear system with a parameter, J. Math.
Anal. Appl., 340 (2008), 658–668.
[8] G. Zhang, S.Cheng, Existence of solutions for a nonlinear system with parameter, J. Math.
Anal. Appl. 314 (2006), 311–319.
[9] G. Zhang and W. Feng, On the number of positive solutions of a nonlinear algebraic system,
Linear Algebra Appl., 422 (2007), 404–421.
[10] G. Zhang, Existence of non-zero solutions for a nonlinear system with a parameter,Nonlinear
Anal., 66 (2007), 140–146.