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Three positive fixed points of nonlinear operators on ordered Banach spaces. (English) Zbl 1005.47051

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

Δ 2 x(t-1)+f(x(t))=0,forallt[a+1,b+1],

where f: is continuous and f is nonnegative for x0·

47H10Fixed point theorems for nonlinear operators on topological linear spaces
34B15Nonlinear boundary value problems for ODE
39A05General theory of difference equations
47N20Applications of operator theory to differential and integral equations
65J15Equations with nonlinear operators (numerical methods)
65Q05Numerical methods for functional equations (MSC2000)