The non-existence and existence of non-constant positive solutions for a diffusive autocatalysis model with saturation

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45)

Cites Work

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Bifurcation and stability analysis of steady states to a Brusselator model
Hopf bifurcation in a reaction-diffusion model with Degn-Harrison reaction scheme
Steady-state and Hopf bifurcations in the Langford ODE and PDE systems
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Hopf bifurcation in general Brusselator system with diffusion
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Point-condensation for a reaction-diffusion system
Size adaptation of Turing prepatterns
Creation of spatial structure by an electric field applied to an ionic cubic autocatalator system
Turing instability and formation of temporal patterns in a diffusive bimolecular model with saturation law
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Diffusion, self-diffusion and cross-diffusion
Persistence and bifurcation of degenerate solutions
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Steady-state bifurcation and Hopf bifurcation for a diffusive Leslie-Gower predator-prey model
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Turing instability of the periodic solutions for the diffusive Sel'kov model with saturation effect
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Bifurcation and Turing pattern formation in a diffusive ratio-dependent predator-prey model with predator harvesting
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Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
Qualitative analysis on positive steady-states for an autocatalytic reaction model in thermodynamics
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Pattern formation in a general glycolysis reaction-diffusion system
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Global Structure of Bifurcating Solutions of Some Reaction-Diffusion Systems
Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
Bounds for the Steady-State Sel'kov Model for Arbitrarypin Any Number of Dimensions
Bifurcation analysis of a diffusive predator-prey model with Beddington-DeAngelis functional response

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