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By analyzing some properties of the linear difference operator A:[Ax](t)=x(t)−Cx(t−τ) first, and then using an extension of Mawhin’s continuation theorem, a second order p-Laplacian neutral functional differential system as follows ddtϕp[(x(t)−Cx(t−τ))′]=f(t,x(t),x(t−μ(t)),x′(t)) is studied. Some new results on the existence of periodic solutions is obtained. The result is related to the deviating...
By means of Mawhin’s continuation theorem, a kind of p-Laplacian Liénard differential equation with a deviating argument as follows: (ϕp(y′(t)))′=f(y(t))y′(t)+h(y(t))+g(y(t−τ(t)))+e(t) is studied. A new result on the existence of periodic solutions is obtained. The interest is that the relation between the existence of periodic solutions and the deviating argument τ(t) is investigated. Meanwhile,...
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