Nontrivial solutions of predator–prey systems with small diffusion

DOI10.1016/0362-546X(87)90035-6zbMath0631.92014OpenAlexW1973568882WikidataQ115599073 ScholiaQ115599073MaRDI QIDQ3768732

Kenneth J. Brown

Publication date: 1987

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(87)90035-6

zbMATH Keywords

Dirichlet boundary conditionsstationary solutionpredator-prey systemindefinite weight functionexistence of nontrivial solutions

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Nonlinear elliptic equations (35J60) Bifurcations in context of PDEs (35B32)

Related Items (14)

Analysis on bifurcation for a predator-prey model with Beddington-DeAngelis functional response and non-selective harvesting ⋮ Positive periodic solutions of predator-prey reaction-diffusion systems ⋮ Permanence in ecological systems with spatial heterogeneity ⋮ Qualitative analysis on a reaction-diffusion model arising from population dynamics ⋮ Coexistence states of a predator-prey model with cross-diffusion ⋮ Some uniqueness and exact multiplicity results for a predator-prey model ⋮ Global positive coexistence of a nonlinear elliptic biological interacting model ⋮ Dynamic behaviors of a predator-prey model with weak additive Allee effect on prey ⋮ On the uniqueness and ordering of steady states of predator-prey systems ⋮ Existence of positive solutions for a prey-predator model with refuge and diffusion ⋮ Analysis on the existence of the steady-states for an ecological-mathematical model with predator-prey-dependent functional response ⋮ \(S\)-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model ⋮ The coexistence states of a predator-prey model with nonmonotonic functional response and diffusion ⋮ Positive solutions of a predator-prey model with cross-diffusion

Cites Work

• On the existence of positive eigenfunctions for an eigenvalue problem with indefinite weight function
• Stability and bifurcation of steady-state solutions for predator-prey equations
• On Positive Solutions of Some Pairs of Differential Equations
• Bifurcation of steady-state solutions in predator-prey and competition systems
• On some linear and nonlinear eigenvalue problems with an indefinite weight function

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