NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION

Acta mathematica scientia,Series B ›› 1995, Vol. 15 ›› Issue (3): 295-302.

Previous Articles Next Articles

NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION

Li Dahua

Dept. of Math., Huazhong Univ. of Sci. & Tech., Wuhan 430074, China

Received:1993-06-17 Revised:1994-04-12 Online:1995-09-25 Published:1995-09-25
Supported by:
The project supported by National Natural Science Foundation of China.

Abstract

Abstract: We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and indefinite weight function,we prove the existence and uniqueness of solutions which are positive in both u and v and asymptotically stable corresponding to the case where the populations can co-exist.

Key words: competitive-diffusive system, bifurcation, indefinite weight function, coexistence

Li Dahua. NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION[J].Acta mathematica scientia,Series B, 1995, 15(3): 295-302.

Trendmd

[1]	Rakesh KUMAR, Anuj Kumar SHARMA, Kulbhushan AGNIHOTRI. STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL [J]. Acta mathematica scientia,Series B, 2018, 38(2): 709-732.
[2]	Suiming SHANG, Yu TIAN, Yajing ZHANG. FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY [J]. Acta mathematica scientia,Series B, 2017, 37(6): 1705-1726.
[3]	Soumaya SÂANOUNI, Nihed TRABELSI. A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION [J]. Acta mathematica scientia,Series B, 2016, 36(6): 1731-1746.
[4]	Yoshiaki MUROYA, Eleonora MESSINA, Elvira RUSSO, Antonia VECCHIO. COEXISTENCE FOR MULTIPLE LARGEST REPRODUCTION RATIOS OF A MULTI-STRAIN SIS EPIDEMIC MODEL [J]. Acta mathematica scientia,Series B, 2016, 36(5): 1524-1530.
[5]	CHEN Hui-Qin, DUAN Jin-Qiao, ZHANG Cheng-Jian. ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LÉVY NOISES [J]. Acta mathematica scientia,Series B, 2012, 32(4): 1391-1398.
[6]	LONG Jing, YANG Jian-Fu. POSITIVE SOLUTIONS FOR WEAKLY COUPLED NONLINEAR ELLIPTIC SYSTEMS [J]. Acta mathematica scientia,Series B, 2010, 30(5): 1577-1592.
[7]	Li Yangcheng; He Wei. VERSAL UNFOLDING OF EQUIVARIANT BIFURCATION PROBLEMS IN MORE GENERAL CASE UNDER TWO EQUIVALENT GROUPS [J]. Acta mathematica scientia,Series B, 2008, 28(4): 915-923.
[8]	Li Jianquan; Ma Zhien; Zhou Yicang. GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA [J]. Acta mathematica scientia,Series B, 2006, 26(1): 83-93.
[9]	LIU Heng-Xin, ZHANG San-Mu. (r,s)-STABILITY OF UNFOLDING OF \|$\Gamma$-EQUIVARIANT PROBLEM [J]. Acta mathematica scientia,Series B, 2005, 25(3): 408-418.
[10]	Gao Shouping, Li Yangcheng. THE UNFOLDING OF EQUIVARIANT BIFURCATION PROBLEMS WITH PARAMETERS SYMMETRY [J]. Acta mathematica scientia,Series B, 2004, 24(4): 623-632.
[11]	ZHANG Zheng-Jie, LEI Wei-Meng. BIFURCATION RESULTS FOR A SEMILINEAR SCHR¨\|ODINGER EQUATION WITH INDEFINITE LINEAR PART 1 [J]. Acta mathematica scientia,Series B, 2004, 24(3): 493-498.
[12]	MA Li. BIFURCATION IN PRESCRIBED MEAN CURVATURE PROBLEM [J]. Acta mathematica scientia,Series B, 2002, 22(4): 526-532.
[13]	WANG He-Yuan, LI Kai-Tai. NUMERICAL APPROXIMATIONS OF A SEMI-LINEAR ELLIPTIC PROBLEM [J]. Acta mathematica scientia,Series B, 2000, 20(2): 175-180.
[14]	ZHENG Lian-Cun, MA Lian-Xi, HE Ji-Cheng. BIFURCATION SOLUTIONS TO A BOUNDARY LAYER PROBLEM ARISING IN THE THEORY OF POWER LAW FLUIDS [J]. Acta mathematica scientia,Series B, 2000, 20(1): 19-26.
[15]	Zou Jiancheng. FINITE DETERMINATION OF BIFURCATION PROBLEMS [J]. Acta mathematica scientia,Series B, 1998, 18(4): 399-403.

NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10