The authors consider the existence of periodic solutions for Lazer-McKenna suspension bridge equation with damping and nonconstant load:
where . This paper discusses the relationship between the spring constant and the damping , which guarantees the existence of the sign-changing periodic solution under the case that is single-sign, by using Lyapunov-Schmidt reduction methods. The result answers partly the open problem in A. C. Lazer and P. J. McKenna [SIAM Rev. 32, 537-578 (1990; Zbl 0725.73057)].