Abstract
We study the existence, uniqueness, and stability of coexistence states in the Lotka-Volterra model with diffusion for two competing species. We assume that the parameters describing the interaction and self-limitation of the species are constant, and consider two types of growth and boundary conditions: periodic growth rates with Neumann boundary conditions, and constant growth rates with Dirichlet boundary conditions. The main tools for our investigations are existence and comparison theorems based on the maximum principle, upper and lower solutions, and the variational characterization of eigenvalues.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1112-1132 |
| Number of pages | 21 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 44 |
| Issue number | 6 |
| State | Published - Dec 1984 |
Fingerprint
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
STABLE COEXISTENCE IN THE VOLTERRA-LOTKA COMPETITION MODEL WITH DIFFUSION. / Cosner, George; Lazer, A. C.
In: SIAM Journal on Applied Mathematics, Vol. 44, No. 6, 12.1984, p. 1112-1132.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - STABLE COEXISTENCE IN THE VOLTERRA-LOTKA COMPETITION MODEL WITH DIFFUSION.
AU - Cosner, George
AU - Lazer, A. C.
PY - 1984/12
Y1 - 1984/12
N2 - We study the existence, uniqueness, and stability of coexistence states in the Lotka-Volterra model with diffusion for two competing species. We assume that the parameters describing the interaction and self-limitation of the species are constant, and consider two types of growth and boundary conditions: periodic growth rates with Neumann boundary conditions, and constant growth rates with Dirichlet boundary conditions. The main tools for our investigations are existence and comparison theorems based on the maximum principle, upper and lower solutions, and the variational characterization of eigenvalues.
AB - We study the existence, uniqueness, and stability of coexistence states in the Lotka-Volterra model with diffusion for two competing species. We assume that the parameters describing the interaction and self-limitation of the species are constant, and consider two types of growth and boundary conditions: periodic growth rates with Neumann boundary conditions, and constant growth rates with Dirichlet boundary conditions. The main tools for our investigations are existence and comparison theorems based on the maximum principle, upper and lower solutions, and the variational characterization of eigenvalues.
UR - http://www.scopus.com/inward/record.url?scp=0021618680&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0021618680&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0021618680
VL - 44
SP - 1112
EP - 1132
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 6
ER -