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Qualitative analysis of a ratio-dependent predator–prey system with diffusion
Ratio-dependent predator–prey models are favoured by many animal ecologists recently as they better describe predator–prey interactions where predation involves a searching process. When densities ofExpand
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Strategy and stationary pattern in a three-species predator–prey model
Abstract In this paper, we study a strongly coupled system of partial differential equations which models the dynamics of a two-predator-one-prey ecosystem in which the prey exercises a defenseExpand
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Global existence of a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant
Abstract This paper deals with the cancer invasion model { u t = Δ u − χ ∇ ⋅ ( u ∇ v ) − ξ ∇ ⋅ ( u ∇ w ) + μ u ( 1 − u − w ) , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , w t = − v w + η w (Expand
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Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion
This paper deals with non-constant positive steady-state solutions of a predator-prey system with non-monotonic functional response, also called Holling type-IV interaction terms, and diffusion underExpand
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Time periodic solutions of the diffusive Nicholson blowflies equation with delay
Abstract This paper is concerned with the Nicholson blowflies equation with nonlinear diffusion and time delay subject to the homogeneous Dirichlet boundary condition in a bounded domain. WeExpand
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Existence of global solutions for a three‐species predator‐prey model with cross‐diffusion
In this short note, we study a strongly coupled system of partial differential equations which models the dynamics of a two-predator-one-prey ecosystem in which the prey exercises defense switchingExpand
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Boundary blow-up solutions of p-Laplacian elliptic equations with lower order terms
We study the existence, uniqueness, and asymptotic behavior of blow-up solutions for a general quasilinear elliptic equation of the type −Δpu = a(x)um−b(x)f(u) with p >  1 and 0 <  m <  p−1. The mainExpand
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Existence and non-existence of global solutions for a higher-order semilinear parabolic system
In this paper, we study the higher-order semilinear parabolic system u t + (-Δ) m u = |v| p , (t, x) ∈ R 1 + × R N , v t + (-Δ) m v = |u| q , (t, x) ∈ R 1 + × R N , u(0, x) = u 0 (x), v(0, x) = v 0Expand
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Qualitative analysis of a diffusive variable-territory prey-predator model
In this paper, we study the variable-territory prey-predator model. We first establish the global stability of the unique positive constant steady state for the ODE system and the reactionExpand
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Sharp spatial patterns of the diffusive Holling-Tanner prey-predator model in heterogeneous environment
This paper studies positive steady-state solutions of the diffusive Holling-Tanner prey-predator model in heterogeneous environments subject to the homogeneous Neumann boundary condition. InExpand
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