Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

Abstract EN

By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))], t≠tk, k∈Z+; x(tk+)=x(tk-)+θk(x(tk)), k∈Z+.

As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.