Abstract: This paper is concerned with the existence and multiplicity of the solutions for the fourth-order boundary value problem , , , where is continuous, and are parameters. Using the variational structure of the above boundary value problem and critical point theory, it is shown that the different locations of the pair and lead to different existence results for the above boundary value problem. More precisely, if the pair is on the left side of the first eigenvalue line, then the above boundary value problem has only the trivial solution for and has infinitely many solutions for ; if is on the right side of the first eigenvalue line and , then the above boundary value problem has two nontrivial solutions or has at least distinct pairs of solutions, which depends on the fact that the pair is located in the second or fourth (first) quadrant. [Copyright &y& Elsevier]