Oscillatory and monotone solutions of first-order nonlinear delay differential equations

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Nino Partsvania ◽  
Zaza Sokhadze

AbstractFor first order nonlinear delay differential equations, necessary and sufficient conditions are established for the oscillation of all proper solutions as well as for the existence of at least one vanishing at infinity proper Kneser solution.

2007 ◽  
Vol 49 (2) ◽  
pp. 197-211 ◽  
Author(s):  
CH. G. PHILOS

AbstractSecond order nonlinear delay differential equations with positive delays are considered, and sufficient conditions are given that guarantee the existence of positive increasing solutions on the half-line with first order derivatives tending to zero at infinity. The approach is elementary and is essentially based on an old idea which appeared in the author's paper Arch. Math. (Basel)36 (1981), 168–178. The application of the result obtained to second order Emden-Fowler type differential equations with constant delays and, especially, to second order linear differential equations with constant delays, is also presented. Moreover, some (general or specific) examples demonstrating the applicability of the main result are given.


2016 ◽  
Vol 14 (1) ◽  
pp. 361-369 ◽  
Author(s):  
Božena Dorociaková ◽  
Rudolf Olach

AbstractThe paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered.


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