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

Abstract

In this paper, by using the continuation theorem of coincidence degree theory, we study a kind of high-order p -Laplacian differential equation as follows: ( φ p ( 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 ) 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.