Open AccessFixed Point Theory and Positive Solutions for a Ratio-Dependent Elliptic System
Author(s) -
Jingmei Liu,
Aixia Qian
Publication year - 2019
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.579
H-Index - 28
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2019/2193670
Subject(s) - fixed point index , mathematics , dirichlet boundary condition , bifurcation theory , fixed point , fixed point theorem , degree (music) , mathematical analysis , zero (linguistics) , bifurcation , boundary value problem , asymptotic analysis , boundary (topology) , dirichlet distribution , nonlinear system , physics , quantum mechanics , linguistics , philosophy , acoustics
We consider a ratio-dependent predator-prey model under zero Dirichlet boundary condition. By using topological degree theory and fixed index theory, we study the necessary and sufficient conditions for the existence of positive solutions. Then we present the asymptotic behavior analysis of positive solutions, by bifurcation theory and energy estimates.