GROWTH CONDITIONS FOR UNIQUENESS OF SMOOTH POSITIVE SOLUTIONS TO AN ELLIPTIC MODEL

TitleGROWTH CONDITIONS FOR UNIQUENESS OF SMOOTH POSITIVE SOLUTIONS TO AN ELLIPTIC MODEL
Publication TypeJournal Article
Year of Publication2016
AuthorsKANG, JOONH
Secondary TitleCommunications in Applied Analysis
Volume20
Issue4
Start Page575
Pagination10
Date Published11/2016
Type of Workscientific: mathematics
ISSN1083-2564
AMS35Jxx
Abstract

The uniqueness of positive solution to the elliptic model

∆u + u[a + g(u, v)] = 0 in Ω,
∆v + v[a + h(u, v)] = 0 in Ω,
u = v = 0 on ∂Ω,

were investigated.

URLhttp://www.acadsol.eu/en/articles/20/4/7.pdf
DOI10.12732/caa.v20i4.7
Short TitlePositive Solutions to an Elliptic Model
Alternate JournalCAA
Refereed DesignationRefereed
Full Text

REFERENCES

[1] S.W. Ali and C. Cosner, On the uniqueness of the positive steady state for LotkaVolterra Models with diffusion, Journal of Mathematical Analysis and Application, 168 (1992), 329-341, doi:10.1016/0022-247X(92)90161-6
[2] R.S. Cantrell and C. Cosner, On the steady-state problem for the Volterra-Lotka competition model with diffusion, Houston Journal of Mathematics, 13 (1987), 337-352. 
[3] R.S. Cantrell and C. Cosner, On the uniqueness and stability of positive solutions in the Volterra-Lotka competition model with diffusion, Houston J. Math., 15 (1989) 341-361.
[4] C. Cosner and A. C. Lazer, Stable coexistence states in the Volterra-Lotka competition model with diffusion, Siam J. Appl. Math., 44 (1984), 1112-1132.
[5] D. Dunninger, Lecture Note for Applied Analysis, Michigan State University.
[6] C. Gui and Y. Lou, Uniqueness and nonuniqueness of coexistence states in the Lotka-Volterra competition model, Comm Pure and Appl. Math., XVL2, No. 12 (1994), 1571-1594.
[7] J. L.-Gomez and R. Pardo, Existence and uniqueness for some competition models with diffusion, C.R. Acad. Sci. Paris, Ser. I Math., 313 (1991), 933-938.
[8] J. Kang, Positive equibibrium solutions to general population model, International Journal of Pure and Applied Mathematics, 85, No. 6 (2013), 1009-1019, doi: http://dx.doi.org/10.12732/ijpam.v85i6.4.
[9] J. Kang and Y. Oh, A sufficient condition for the uniqueness of positive steady state to a reaction diffusion system, Journal of Korean Mathematical Society, 39, No. 39 (2002), 377-385.
[10] J. Kang and Y. Oh, Uniqueness of coexistence state of general competition model for several competing species, Kyungpook Mathematical Journal, 42, No. 2 (2002), 391-398.
[11] J. Kang, Y. Oh, and J. Lee, The existence, nonexistence and uniqueness of global positive coexistence of a nonlinear elliptic biological interacting model, Kangweon-Kyungki Math. Jour., 12, No. 1 (2004), 77-90.
[12] P. Korman and A. Leung, A general monotone scheme for elliptic systems with applications to ecological models, Proceedings of the Royal Society of Edinburgh, 102A (1986), 315-325
[13] P. Korman and A. Leung, On the existence and uniqueness of positive steady states in the Volterra-Lotka ecological models with diffusion, Applicable Analysis, 26, 145-160, http://dx.doi.org/10.1080/00036818708839706.
[14] L. Li and R. Logan, Positive solutions to general elliptic competition models, Differential and Integral Equations, 4 (1991), 817-834. 
[15] A. Leung, Equilibria and stabilities for competing-species, reaction-diffusion equations with Dirichlet boundary data, J. Math. Anal. Appl., 73 (1980), 204-218.