摘要：In this paper, we consider the following high-order p-Laplacian generalized neutral differential equation ( φ p ( x ( t ) − c x ( t − δ ( t ) ) ) ′ ) ( n − 1 ) + g ( t , x ( t ) , x ( t − τ ( t ) ) , x ′ ( t ) ) = e ( t ) , where p ≥ 2 , φ p ( x ) = x p − 2 x for x ≠ 0 and φ p ( 0 ) = 0 ; g : R 4 → R is a continuous periodic function with g ( t + T , ⋅ , ⋅ , ⋅ ) ≡ g ( t , ⋅ , ⋅ , ⋅ ) , and g ( t , a , a , 0 ) − e ( t ) ≢ 0 for all a ∈ R . e : R → R is a continuous periodic function with e ( t + T ) ≡ e ( t ) and ∫ 0 T e ( t ) d t = 0 , c is a constant and c ≠ 1 , δ ∈ C 1 ( R , R ) and δ is a T-periodic function, T is a positive constant; n is a positive integer. By applications of coincidence degree theory and some analysis skills, sufficient conditions for the existence of periodic solutions are established. MSC:34K13, 34K40, 34C25.
