Stability and uniqueness for cooperative degenerate Lotka-Volterra model

DOI10.1016/S0362-546X(01)00138-9zbMath1043.35078MaRDI QIDQ1601669

Antonio Suárez, Manuel Delgado

Publication date: 27 June 2002

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

zbMATH Keywords

sub- and supersolutionsblow-up in finite timepositive steady statecooperative degenerate Lotka-Volterra modelorder preserving properties

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (7)

A Lotka-Volterra cooperating reaction-diffusion system with degenerate density-dependent diffusion ⋮ Qualitative properties of a cooperative degenerate Lotka-Volterra model ⋮ Nonnegative solutions for a heterogeneous degenerate competition model ⋮ Periodic solutions for the degenerate Lotka-Volterra competition system ⋮ Asymptotic behavior of solutions for a Lotka-Volterra mutualism reaction-diffusion system with time delays ⋮ Dynamics of Lotka-Volterra cooperation systems governed by degenerate quasilinear reaction-diffusion equations ⋮ Nonnegative solutions for the degenerate logistic indefinite sublinear equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Attractivity properties of nonnegative solutions for a class of nonlinear degenerate parabolic problems
• Strong positivity in \(C(\bar\Omega)\) for elliptic systems
• The principle of linearized stability of a class of degenerate diffusion equations
• On the diffusion of biological populations
• Invariant sets and existence theorems for semilinear parabolic and elliptic systems
• The maximum principle for cooperative weakly coupled elliptic systems and some applications
• Combined effects of concave and convex nonlinearities in some elliptic problems
• Elliptic systems with nonlinear diffusion in population dynamics
• The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems
• On the symbiotic Lotka-Volterra model with diffusion and transport effects
• Stabilization of solutions of a degenerate nonlinear diffusion problem
• On the dirichlet problem for elliptic systems
• Support properties of solutions for a class of degenerate parabolic problems
• On the existence and uniqueness of positive steady states in the volterra-lotka ecological models with diffusion
• Dynamics of the lotka-volterra systems with diffusion
• Nonlinear elliptic boundary-value problems in unbounded domains
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• The Minimum Principle for Elliptic Systems
• On the existence of dead cores for degenerate Lotka—Volterra models
• Necessary and sufficient condition for the existence of positive solutions of certain cooperative system
• Existence of solutions for elliptic systems with Hölder continuous nonlinearities

This page was built for publication: Stability and uniqueness for cooperative degenerate Lotka-Volterra model