Nonlocal problems arising from the birth-jump processes

2018 ◽  
Vol 149 (2) ◽  
pp. 447-469
Author(s):  
M. Delgado ◽  
A. Suárez ◽  
I. B. M. Duarte
Keyword(s):  
Positive Solution ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Solution Method ◽  
Eigenvalue Problems ◽  
Logistic Equation ◽  
Jump Processes ◽  
Nonlocal Problems

In this paper, we prove the existence and uniqueness of a positive solution for a nonlocal logistic equation arising from the birth-jump processes. For this, we establish a sub-super solution method for nonlocal elliptic equations, we perform a study of the eigenvalue problems associated with these equations and we apply these results to the nonlocal logistic equation.

scholarly journals Unbounded principal eigenfunctions and the logistic equation on RN

2003 ◽  
Vol 67 (3) ◽  
pp. 413-427 ◽  
Author(s):  
Wei Dong ◽  
Yihong Du
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Eigenvalue Problems ◽  
Growth Conditions ◽  
Logistic Equation ◽  
Exponential Rate ◽  
Unique Positive Solution ◽  
Unbounded Coefficients ◽  
Growth Restrictions

We consider the logistic equation − Δu = a (x) u − b (x) up on all of RN with possibly unbounded coefficients near infinity. We show that under suitable growth conditions of the coefficients, the behaviour of the positive solutions of the logistic equation can be largely determined. We also show that certain linear eigenvalue problems on all of RN have principal eigenfunctions that become unbounded near infinity at an exponential rate. Using these results, we finally show that the logistic equation has a unique positive solution under suitable growth restrictions for its coefficients.

scholarly journals On Dynamical Behavior of Discrete Time Fuzzy Logistic Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Qianhong Zhang ◽  
Fubiao Lin
Keyword(s):  
Difference Equation ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Fuzzy Numbers ◽  
Dynamical Behavior ◽  
Logistic Equation ◽  
State Variables ◽  
Initial Value ◽  
Numerical Examples ◽  
Logistic Difference Equation

The aim of this paper is to investigate the dynamical behavior of the following model which describes the logistic difference equation taking into account the subjectivity in the state variables and in the parameters. xn+1=Axn(1~-xn),  n=0,1,2,⋯, where {xn} is a sequence of positive fuzzy numbers. A,1~ and the initial value x0 are positive fuzzy numbers. The existence and uniqueness of the positive solution and global asymptotic behavior of all positive solution of the fuzzy logistic difference equation are obtained. Moreover, some numerical examples are presented to show the effectiveness of results obtained.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

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