摘要：The existence of the nontrivial periodic solutions for the nonautonomous first order delay differential equation x ′ ( t ) = − [ f ( t , x ( t − 1 ) ) + f ( t , x ( t − 2 ) ) + ⋯ + f ( t , x ( t − ( 2 N − 1 ) ) ) ] $x'(t)=-[f(t, x(t-1))+f(t, x(t-2))+\cdots+f(t, x(t-(2N-1)))]$ is investigated, where f ∈ C ( R × R , R ) $f\in C({\mathbf{R}}\times{\mathbf{R}}, {\mathbf{R}})$ is 2N-periodic in t and odd in x, N is a positive integer. We prove several new existence results by some recent critical point theorems.
关键词：first order delay differential equation ; nonautonomous ; periodic solution ; critical point theorems
