THE EXISTENCE OF PERIODIC SOLUTIONS FOR A KIND OF HIGH-ORDER DUFFING EQUATIONS WITH SIGN-CHANGING COEFFICIENT AHEAD OF NONLINEAR TERM
一类非线性项前系数可变号的高阶Duffing方程的周期解存在性问题

In this paper, by using the theory of Fourier series, Bernoulli number theory and continuation theorem of coincidence degree theory, we study a kind of high-order functional differential equation with a deviating argument as follows:x^{(m)}(t)+\beta (t)g(x(t-\tau(t)))=p(t). Some new results on the existence of periodic solutions are obtained. Here the sign of \beta(t) can be changed. But, the methods to estimate a priori bounds of periodic solutions are different from the corresponding ones of the past.