Abstract
In this paper, we investigate the existence and stability of the positivesteady-state solutions for a Lotka-Volterra system with intraspecific competition byusing the Lyapunov-Schmidt reduction technique. To do this, we must firstly obtainthe semi-trivial steady states as their base, which extend the method used in theprevious studies. Our results show that the two competition species withintraspecific competition can coexist for bigger regions of the diffusion rateμ and also complete the existing works. MSC: 35K57.
Highlights
The maintenance of biodiversity has received increasing attention from ecologists and mathematicians
Resource competition is thought as an important factor in driving evolutionary diversification, in which intraspecific competition for resources plays a major role; see [ – ]
In Section, on the basis of the semi-trivial solutions obtained in Section, we investigate the existence and nonexistence of positive steady-state solutions of ( . ) by using the Lyapunov-Schmidt reduction technique, the implicit function theorem and the finite covering theorem
Summary
The maintenance of biodiversity has received increasing attention from ecologists and mathematicians. Our main purpose is to study the existence and stability of the positive steady-state solutions (that is, the coexistence states) of We must firstly get the semi-trivial steady-state solutions of
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