By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for th order delay differential equations with damping terms . Some new results on the existence of periodic solutions of the investigated equation are obtained.
The authors use coincidence degree theory to establish some new results on the existence of T-periodic solutions for the delay differential equation x''(t) + a₁x'(t) + a₂(xⁿ(t))' + a₃x(t)+ a₄x(t-τ) + a₅xⁿ(t) + a₆xⁿ(t-τ) = f(t), which appears in a model of a power system. These results are of practical significance.
Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem of Krasnoselskii....
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.