Three positive fixed points of nonlinear operators on ordered Banach spaces (Q1600376)

The authors generalize the triple fixed-point theorem of Leggett and Williams, which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a Banach space. As an application of the abstract result, the authors prove the existence of three positive symmetric solutions of the discrete second-order nonlinear conjugate boundary value problem \[ \Delta^2 x(t-1)+f(x(t))=0, \text{for all} t\in [a+1,b+1], \] \[ x(a)=0=x(b+2), \] where \(f: \mathbb R\to \mathbb R\) is continuous and \(f\) is nonnegative for \(x\geq 0.\)