Existence and uniqueness of periodic solutions for a kind of high-order pp-Laplacian Duffing differential equation with sign-changing coefficient ahead of linear term

In this paper, by using the continuation theorem of coincidence degree theory, we study a kind of high-order pp-Laplacian differential equation as follows: (φp(y(m)(t)))(m)+β(t)y′(t)+g(t,y(t))=e(t).(φp(y(m)(t)))(m)+β(t)y′(t)+g(t,y(t))=e(t). Some new results on the existence and uniqueness of periodic solutions are obtained. The interesting thing is that the coefficient β(t)β(t) is allowed to change sign, which could be achieved infrequently in previous papers. But, the methods to estimate a priori bounds of periodic solutions are different from the corresponding ones used in the past.