摘要：In this paper, we first discuss some properties of the neutral operator with multiple delays and variable coefficients ( A x ) ( t ) : = x ( t ) − ∑ i = 1 n c i ( t ) x ( t − δ i ) $(Ax)(t):=x(t)-\sum_{i=1}^{n}c_{i}(t)x(t-\delta _{i})$ . Afterwards, by using an extension of Mawhin’s continuation theorem, a second order p-Laplacian neutral differential equation ( ϕ p ( x ( t ) − ∑ i = 1 n c i ( t ) x ( t − δ i ) ) ′ ) ′ = f ˜ ( t , x ( t ) , x ′ ( t ) ) $$ \Biggl(\phi _{p} \Biggl(x(t)-\sum_{i=1}^{n}c_{i}(t)x(t- \delta _{i}) \Biggr)' \Biggr)'=\tilde{f} \bigl(t,x(t),x'(t)\bigr) $$ is studied. Some new results on the existence of a periodic solution are obtained. Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from those known in the literature.
关键词：Neutral operator ; p -Laplacian ; Periodic solution ; Extension of Mawhin’s continuation theorem ; Singularity
