Non-negative Steady State Solutions to an Elliptic Biological Model

Brian Ibanez; Joon Hyuk Kang; Jungho Lee

Non-negative Steady State Solutions to an Elliptic Biological Model

Brian Ibanez
, Joon Hyuk Kang
, Jungho Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The non-existence and existence of positive solutions for the generalized predator-prey biological model for two species of animals Δu + ug(u,v) = 0 in Ω, Δv + vh(u,v) = 0 in Ω, u = v = 0 on ∂Ω, is investigated in this paper. The techniques used in this paper are from elliptic theory, the upper-lower solution method, the maximum principles and spectrum estimates. The arguments also rely on detailed properties of solutions to logistic equations.

Original language	American English
Pages (from-to)	385-394
Journal	International Journal of Pure and Applied Mathematics
Volume	53
Issue number	3
State	Published - Dec 2009

Keywords

Generalized predator-prey biological model
Logistic equations
Maximum principles
Non-existence and existence of positive solutions

Disciplines

Mathematics

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Non-negative Steady State Solutions to an Elliptic Biological ModFinal published version, 135 KBLicense: Unspecified

Cite this

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title = "Non-negative Steady State Solutions to an Elliptic Biological Model",

abstract = "The non-existence and existence of positive solutions for the generalized predator-prey biological model for two species of animals Δu + ug(u,v) = 0 in Ω, Δv + vh(u,v) = 0 in Ω, u = v = 0 on ∂Ω, is investigated in this paper. The techniques used in this paper are from elliptic theory, the upper-lower solution method, the maximum principles and spectrum estimates. The arguments also rely on detailed properties of solutions to logistic equations. ",

keywords = "Generalized predator-prey biological model, Logistic equations, Maximum principles, Non-existence and existence of positive solutions",

author = "Brian Ibanez and \{Hyuk Kang\}, Joon and Jungho Lee",

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language = "American English",

volume = "53",

pages = "385--394",

journal = "International Journal of Pure and Applied Mathematics",

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TY - JOUR

T1 - Non-negative Steady State Solutions to an Elliptic Biological Model

AU - Ibanez, Brian

AU - Hyuk Kang, Joon

AU - Lee, Jungho

PY - 2009/12

Y1 - 2009/12

N2 - The non-existence and existence of positive solutions for the generalized predator-prey biological model for two species of animals Δu + ug(u,v) = 0 in Ω, Δv + vh(u,v) = 0 in Ω, u = v = 0 on ∂Ω, is investigated in this paper. The techniques used in this paper are from elliptic theory, the upper-lower solution method, the maximum principles and spectrum estimates. The arguments also rely on detailed properties of solutions to logistic equations.

AB - The non-existence and existence of positive solutions for the generalized predator-prey biological model for two species of animals Δu + ug(u,v) = 0 in Ω, Δv + vh(u,v) = 0 in Ω, u = v = 0 on ∂Ω, is investigated in this paper. The techniques used in this paper are from elliptic theory, the upper-lower solution method, the maximum principles and spectrum estimates. The arguments also rely on detailed properties of solutions to logistic equations.

KW - Generalized predator-prey biological model

KW - Logistic equations

KW - Maximum principles

KW - Non-existence and existence of positive solutions

UR - https://digitalcommons.andrews.edu/pubs/1838

M3 - Article

VL - 53

SP - 385

EP - 394

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

IS - 3

ER -

Non-negative Steady State Solutions to an Elliptic Biological Model

Abstract

Keywords

Disciplines

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