On extraneous solutions with uniformly bounded difference quotients for a discrete analogy of a nonlinear ordinary boundary-value problem

Abstract

For a discrete analogy with n − 1 ∈ N grid points of a nonlinear ordinary boundary-value problem with an implicit differential equation of the second order, the existence of 2n−1−2 extraneus solutions is shown, whose sequences of difference quotients of the first and the second order are uniformly bounded as n → ∞. For selected explicitly represented sequences of extraneous solutions, the limiting function as n → ∞ is explicitly given. These functions either do not solve the differential equatin or only in a non-classical sense.