一类二阶泛函微分方程多个周期解的存在性

Existence of Several Perodic Solution for a Class of Second Order Functional Differential Equations

该文利用Mawhin重合度延拓定理研究了一类二阶泛函微分方程x″(t)+f(t,x(t),x(t-τ(t)))[x′(t)]~n+a(t)x^2(t)+b(t)x(t)=p(t)(n≥2)的多个周期解的问题,得到了这类方程至少存在两个周期解的结果.

By applying the continuation theorem of coincidence degree theory developed by Mawhin,the authors study the existence of several periodic solutions to the second order functional differential equation. x″（t）＋f（t,x（t）,x（t-τ（t）））[x′（t）]^n＋a（t）x^2（t）＋b（t）x（t）=p（t）（n≥2）. Some new results for the existence of at least two periodic solutions to such equation are obtained.