scholarly journals Existence of Positive Solutions for Second-Order Neumann Difference System

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yanqiong Lu ◽  
Ruyun Ma
Keyword(s):  
Positive Solutions ◽  
Principal Eigenvalue ◽  
Linear Part ◽  
Second Order ◽  
Difference System ◽  
Nonnegative Solutions ◽  
Existence Of Positive Solutions ◽  
Existence And Nonexistence ◽  
Linearized System

This paper studies a class of Neumann difference system which is not cooperative but its linear part is and this makes it possible to establish existence and nonexistence results for nonnegative solutions of the system in terms of the principal eigenvalue of the corresponding linearized system.

scholarly journals On a System Modelling a Population with Two Age Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hongliang Gao ◽  
Ruyun Ma
Keyword(s):  
Differential Equations ◽  
Principal Eigenvalue ◽  
Linear Part ◽  
Age Groups ◽  
System Modelling ◽  
Adult Age ◽  
First Order ◽  
Existence And Nonexistence ◽  
Linearized System ◽  
Two Age Groups

A system of first order ordinary differential equations describing a population divided into juvenile and adult age groups is studied. The system is not cooperative but its linear part is, and this makes it possible to establish the existence and nonexistence results of positive solutions for the system in terms of the principal eigenvalue of the corresponding linearized system.

8.—On Second-order Differential Inequalities

1974 ◽  
Vol 72 (2) ◽  
pp. 109-127 ◽  
Author(s):  
F. V. Atkinson
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Second Order ◽  
Differential Inequalities ◽  
Existence Of Positive Solutions ◽  
Image Position

SynopsisThis paper is devoted to a study of differential equations and inequalities of the formandThe results are mainly concerned with the existence of positive solutions, their uniqueness in the case of (*), and bounds for these solutions.

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