The existence of solutions of a nonlinear suspension bridge equation

摘要

We investigate a relation between the multiplicity of solutions and source terms in a nonlinear suspension bridge equation in the interval $left(-dfrac{pi}{2},dfrac{pi}{2}ight),$ under Dirichlet boundary condition, $u_{tt}+u_{xxxx}+bu^+=f(x),$ where the nonlinearity $-(bu^+)$ crosses an eigenvalue $lambda_{10}$ and $f$ is generated by $phi_{00},$ $phi_{10}.$