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Opial Inequalities with Applications in Differential and Difference Equations
Preface. 1: Opial's Inequality. 2: Generalizations of Opial's Inequality. 3: Opial Inequalities Involving Higher Order Derivatives. 4: Opial Inequalities in Several Independent Variables. 5: DiscreteExpand
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Qualitative analysis of a ratio-dependent predator–prey system with diffusion
  • P. Pang, M. Wang
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh…
  • 1 August 2003
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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Sharp Opial-Type Inequalities Involving Higher Order Derivatives of Two Functions
In this paper we shall offer very general Opial-type inequalities involving higher order derivatives of two functions. From these inequalities we then deduce extended and improved versions of severalExpand
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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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Global solutions for a general strongly coupled prey-predator model
TLDR
This work investigates global solutions for a general strongly coupled prey–predator model that involves (self-)diffusion and cross-diffusion, especially in higher spatial dimensions. Expand
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On a generalized difference system
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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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Qualitative Analysis of a Prey-Predator Model with Stage Structure for the Predator
TLDR
In this paper, we propose a diffusive prey-predator model with stage structure for the predator. Expand
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Monotone iterative methods for a general class of discrete boundary value problems
Abstract In this paper we shall offer comparison results as well as monotone iterative schemes for the construction of solutions to a very general class of discrete boundary value problems. TheExpand
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