Summary: In this paper, we establish an equivalent statement to minimax inequality for a special class of functionals. As an application, we prove the existence of three solutions to the Dirichlet problem \[ \displaylines{ -u''(x)+m(x)u(x) =\lambda f(x,u(x)),\quad x\in (a,b),\cr u(a)=u(b)=0, } \] where \(\lambda>0\), \(f:[a,b]\times \mathbb{R}\to \mathbb{R}\) is a continuous function which changes sign on \([a,b]\times \mathbb{R}\) and \(m(x)\in C([a,b])\) is a positive function.