Periodic solutions of a nonlinear suspension bridge equation with damping and nonconstant load ✩

The paper is concerned with the existence of periodic solutions for the Lazer–McKenna suspension bridge equation with damping and nonconstant load. By using the Lyapunov–Schmidt reduction methods, the author discuss the relationship between the sign-changing solutions and the source terms. The result answers partly the open problem in Lazer and McKenna (SIAM Rev. 32 (1990) 537–578).  2003 Elsevier Science (USA). All rights reserved.