Periodic solutions of neutral Duffing equations.
A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.
The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) , where f is T-periodic in t. We construct a pair of subsets of ℝ × ℝⁿ called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.
By using the coincidence degree theory, we study a type of -Laplacian neutral Rayleigh functional differential equation with deviating argument to establish new results on the existence of -periodic solutions.
We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].
We study a generalized Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we employ a novel proof to establish some criteria guaranteeing the permanence of this model. Moreover, we give an example to illustrate our main result.