Abstract
By analyzing some properties of the linear difference operator A : [ A x ] ( t ) = x ( t ) − C x ( t − τ ) first, and then using an extension of Mawhin’s continuation theorem, a second order p -Laplacian neutral functional differential system as follows d d t ϕ p [ ( x ( t ) − C x ( 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 arguments τ and μ . Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature.
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