Bifurcation and monotonicity in competition reaction-diffusion systems

DOI10.1016/0362-546X(94)90248-8zbMath0807.35041OpenAlexW1990408833MaRDI QIDQ4312091

Kenneth J. Brown, Yihong Du

Publication date: 1 March 1995

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

Full work available at URL: https://doi.org/10.1016/0362-546x(94)90248-8

zbMATH Keywords

nonlocal termpositive steady statesdecoupling procedure

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Bifurcations in context of PDEs (35B32)

Related Items (13)

Allee effect and bistability in a spatially heterogeneous predator-prey model ⋮ Positive solutions for a three-species competition system with diffusion—I. General existence results ⋮ Realization of prescribed patterns in the competition model. ⋮ Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates ⋮ A diffusive competition model with a protection zone ⋮ Nonnegative solutions for a heterogeneous degenerate competition model ⋮ Structure of positive solutions for some semilinear elliptic systems where bifurcation from infinity occurs ⋮ Coexistence states in a cross-diffusion system of a competition model ⋮ Analysis on steady states of a competition system with nonlinear diffusion terms ⋮ Bifurcation from semitrivial solution bundles and applications to certain equation systems ⋮ Effects of a degeneracy in the competition model. I: Classical and generalized steady-state solutions ⋮ Effects of a degeneracy in the competition model. II: Perturbation and dynamical behaviour ⋮ A degree theoretic approach to N-species periodic competition systems on the whole ℝ^N

Cites Work

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• On positive solutions of some pairs of differential equations. II
• Bifurcation of steady-state solutions in predator-prey and competition systems
• Stable Coexistence States in the Volterra–Lotka Competition Model with Diffusion
• On the existence and uniqueness of positive steady states in the volterra-lotka ecological models with diffusion
• On the Existence and Uniqueness of Positive Solutions for Competing Species Models with Diffusion

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