scholarly journals Existence and positivity of solutions for a totally nonlinear neutral periodic differential equation

2013 ◽  
Vol 14 (3) ◽  
pp. 757 ◽  
Author(s):  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Periodic Differential Equation ◽  
Positivity Of Solutions

Positivity of solutions of elliptic equations with nonlocal terms

1996 ◽  
Vol 126 (3) ◽  
pp. 643-663 ◽  
Author(s):  
W. Allegretto ◽  
A. Barabanova
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlinear System ◽  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Nonlocal Problem ◽  
Order Partial Differential Equation ◽  
Nonnegative Solutions ◽  
Positivity Of Solutions ◽  
Nonlocal Terms

In this paper we study a nonlocal problem for a second-order partial differential equation which depends on a parametern. We prove the existence of critical values 0 <and 0 >such that for all≦ɳ≦and for all non-negative right-hand sides, our problem has nonnegative solutions. We obtain a formula forɳ0, the maximal possible value of, and find the exact value of ɳ for spherical ɳ. We also study the corresponding eigenvalue problem. At the end of the paper, we consider the application of our results to the nonlinear system describing the distribution of temperature and potential in a microsensor.

scholarly journals The frequencies of almost periodic solutions of almost periodic differential equations

1974 ◽  
Vol 17 (3) ◽  
pp. 332-344
Author(s):  
G. C. O'Brien
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Periodic Differential Equation ◽  
Right Hand

AbstractAlmost periodic solutions of a first order almost periodic differential equation in Rp are shown to have less than p basic frequencies additional to the basic frequencies of the almost periodic right hand of the equation.

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