Coexistence problem for a prey-predator model with density-dependent diffusion

DOI10.1016/j.na.2009.05.014zbMath1239.35052OpenAlexW2011141475WikidataQ115568816 ScholiaQ115568816MaRDI QIDQ425799

Yoshio Yamada, Kousuke Kuto

Publication date: 9 June 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.05.014

zbMATH Keywords

bifurcationa priori estimatecross-diffusioncoexistence steady-statesnonlinear diffusion of fractional type

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Population dynamics (general) (92D25) Abstract bifurcation theory involving nonlinear operators (47J15) Bifurcations in context of PDEs (35B32)

Related Items (16)

Qualitative analysis of a strongly coupled predator-prey system with modified Holling-Tanner functional response ⋮ Positive steady-state solutions for predator-prey systems with prey-taxis and Dirichlet conditions ⋮ Global bifurcation of coexistence states for a prey-taxis system with homogeneous Dirichlet boundary conditions ⋮ Coexistence states of a predator-prey model with cross-diffusion ⋮ On a predator-prey model involving age and spatial structure ⋮ Fish-hook shaped global bifurcation branch of a spatially heterogeneous cooperative system with cross-diffusion ⋮ Effect of cross-diffusion in the diffusion prey-predator model with a protection zone. II ⋮ Predator-prey models with prey-dependent diffusion on predators in spatially heterogeneous habitat ⋮ Local dynamics and coexistence of predator-prey model with directional dispersal of predator ⋮ Positive solutions for Lotka-Volterra competition system with large cross-diffusion in a spatially heterogeneous environment ⋮ Weak-renormalized solutions for predator–prey system ⋮ Stationary problem of a predator-prey system with nonlinear diffusion effects ⋮ Positive solutions for a Lotka-Volterra prey-predator model with cross-diffusion of fractional type ⋮ Coexistence states of a ratio-dependent predator-prey model with nonlinear diffusion ⋮ Spatial patterns of the Holling–Tanner predator–prey model with nonlinear diffusion effects ⋮ Positive solutions of a predator-prey model with cross-diffusion

Cites Work

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• On a predator-prey system with cross diffusion representing the tendency of predators in the presence of prey species
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• BIFURCATION FROM SIMPLE EIGENVALUES AND EIGENVALUES OF GEOMETRIC MULTIPLICITY ONE
• Global existence of solutions to Shigesada-Kawasaki-Teramoto cross-diffusion systems on domains of arbitrary dimensions

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