Semilinear Duffing Equation Collision Periodic Solution

In this paper, we deal with the existence of peridic solutions of the following impact systemAssume that g(x) satisfies the semilinear conditionand p(t) ≤ 0 , . We prove that for any n, m ∈ N, n> 2mβ^1/2, that given impact system has at least one 2mπ-periodic soultion.