Effects of a degeneracy in the competition model. I: Classical and generalized steady-state solutions

DOI10.1006/jdeq.2001.4074zbMath1042.35016OpenAlexW2766024708MaRDI QIDQ1604635

Yihong Du

Publication date: 8 July 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4074

zbMATH Keywords

homogeneous Dirichlet boundary conditionscompetition modelpopulation modelheterogeneous environmental effects

Mathematics Subject Classification ID

Related Items (59)

A diffusive predator-prey model in heterogeneous environment ⋮ Allee effect and bistability in a spatially heterogeneous predator-prey model ⋮ Nondegeneracy and uniqueness for boundary blow-up elliptic problems ⋮ Boundary blow-up solutions to elliptic systems of competitive type ⋮ Uniqueness and layer analysis for boundary blow up solutions ⋮ Bifurcation branch of stationary solutions for a Lotka-Volterra cross-diffusion system in a spatially heterogeneous environment ⋮ Combined effects of the spatial heterogeneity and the functional response ⋮ Effects of a degeneracy in a diffusive predator-prey model with Holling II functional response ⋮ Spatial degeneracy vs functional response ⋮ Exact multiplicity for boundary blow-up solutions ⋮ A diffusive predator-prey model with a protection zone ⋮ Dynamics of Holling-type II prey–predator system with a protection zone for prey ⋮ Existence and uniqueness of positive solutions to the boundary blow-up problem for an elliptic system ⋮ Effect of cross-diffusion on the stationary problem of a Leslie prey-predator model with a protection zone ⋮ Bifurcation branch and stability of stationary solutions of a predator–prey model ⋮ A remark on uniqueness of large solutions for elliptic systems of competitive type ⋮ Large solutions of quasilinear elliptic system of competitive type: existence and asymptotic behavior ⋮ Boundary behavior for large solutions to elliptic equations with singular weights ⋮ Qualitative analysis on a reaction-diffusion model arising from population dynamics ⋮ Qualitative analysis of a Lotka-Volterra predator-prey system with migration ⋮ On inverse problems for several coupled PDE systems arising in mathematical biology ⋮ Realization of prescribed patterns in the competition model. ⋮ Elliptic systems with boundary blow-up: existence, uniqueness and applications to removability of singularities ⋮ Effect of cross-diffusion in the diffusion prey-predator model with a protection zone. II ⋮ Global directed dynamics of a Lotka-Volterra competition-diffusion system ⋮ Positive steady states of the S-K-T competition model with spatially heterogeneous interactions ⋮ Study of an elliptic system arising from angiogenesis with chemotaxis and flux at the boundary ⋮ Metasolutions in cooperative systems ⋮ Effects of degeneracy and response function in a diffusion predator–prey model ⋮ A diffusive competition model with a protection zone ⋮ Positive solutions for a competition model with an inhibitor involved ⋮ Positive solutions of a diffusive prey-predator model in a heterogeneous environment ⋮ Nonnegative solutions for a heterogeneous degenerate competition model ⋮ Positive solutions for Lotka-Volterra competition system with large cross-diffusion in a spatially heterogeneous environment ⋮ Large solutions for an elliptic system of quasilinear equations ⋮ Unbounded connected component of the positive solution set of nonlinear operator equation and its applications ⋮ Bifurcation analysis of the Gierer–Meinhardt system with a saturation in the activator production ⋮ On the effects of migration and spatial heterogeneity on single and multiple species ⋮ Boundary blow-up solutions for a cooperative system of quasilinear equation ⋮ Structure of positive solutions for some semilinear elliptic systems where bifurcation from infinity occurs ⋮ Large solutions for a cooperative elliptic system of \(p\)-Laplacian equations ⋮ Convergence in competition models with small diffusion coefficients ⋮ Structure of boundary blow-up solutions for quasi-linear elliptic problems. II: Small and intermediate solutions ⋮ Protection zone in a diffusive predator-prey model with Ivlev-type functional response ⋮ On steady state of some Lotka-Volterra competition-diffusion-advection model ⋮ Symmetry results of large solutions for semilinear cooperative elliptic systems ⋮ Boundary blow-up solutions of cooperative systems ⋮ Steady-State Problem of an S-K-T Competition Model with Spatially Degenerate Coefficients ⋮ Effect of a protection zone in the diffusive Leslie predator-prey model ⋮ On a Lotka-Volterra competition diffusion model with advection ⋮ Effects of protection zone and nonlinear growth on a predator-prey model ⋮ An elliptic system with bifurcation parameters on the boundary conditions ⋮ Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems ⋮ The effects of dispersal and spatial heterogeneity on the dynamics of a predator-prey model ⋮ Coexistence states of a Holling type II predator-prey system with self and cross-diffusion terms ⋮ Long-time behavior of a cooperative periodic-parabolic system: temporal degeneracy versus spatial degeneracy ⋮ Effects of a degeneracy in the competition model. II: Perturbation and dynamical behaviour ⋮ Long-time behavior of a cooperative periodic-parabolic system in a spatiotemporally degenerate environment ⋮ Superlinear indefinite systems: beyond Lotka-Volterra models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On positive solutions of some pairs of differential equations. II
• \(S\)-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model
• First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs
• Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs
• Coexistence in the competition model with diffusion
• Competing species equations with diffusion, large interactions, and jumping nonlinearities
• On the structure of the permanence region for competing species models with general diffusivities and transport effects
• Models for the effects of individual size and spatial scale on competition between species in heterogeneous environments
• Positive solutions with prescribed patterns in some simple semilinear equations
• Positive steady-state solutions of a competing reaction-diffusion system
• A counterexample on competing species equations
• Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equations
• Ecological models, permanence and spatial heterogeneity
• Bifurcation from simple eigenvalues
• Stability and convergence in strongly monotone dynamical systems.
• Bifurcation of steady-state solutions in predator-prey and competition systems
• Stable Coexistence States in the Volterra–Lotka Competition Model with Diffusion
• A general monotone scheme for elliptic systems with applications to ecological models
• Global Bifurcation of Positive Solutions in Some Systems of Elliptic Equations
• On the Existence and Uniqueness of Positive Solutions for Competing Species Models with Diffusion
• On an abstract competition model and applications
• On the Positive Solutions of Semilinear Equations Δu + λu - hu p = 0 on the Compact Manifolds
• Bifurcation and monotonicity in competition reaction-diffusion systems
• Some uniqueness and exact multiplicity results for a predator-prey model
• Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
• Coexistence States and Global Attractivity for Some Convective Diffusive Competing Species Models
• Uniqueness, multiplicity and stability for positive solutions of a pair of reaction–diffusion equations
• Should a Park Be an Island?

This page was built for publication: Effects of a degeneracy in the competition model. I: Classical and generalized steady-state solutions