Search

Using the Leggett-Williams fixed point theorem in cones, we prove the existence of at least three positive solutions to the nonlinear n-th order m-point boundary-value problem Δnu(k) + a(k)f(k, u) = 0, k ∈ {0,N}, u(0) = 0, Δu(0) = 0, . . . ,Δn-2u(0) = 0, u(N + n) = ∑m-2i=1 αiu(ξi). [ABSTRACT FROM AUTHOR]

The article establishes the existence of three positive solutions for second-order discrete boundary value problems. Some background materials and definitions that will be needed in the discussion are presented, which include the definitions of an operator and a nonnegative continuous concave functional on a cone. This paper depends on an application of a fixed-point theorem which deals with fixed points of a cone-preserving operator defined on an ordered Branach space to obtain results. An example is also given to illustrate the main results.