A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with -Laplacian

Abstract: In this paper, we consider the existence of positive solutions for a class of singular fourth-order -Laplacian equation with multi-point boundary conditions. By means of a monotone iterative technique, a necessary and sufficient condition for the existence of a pseudo- positive solution is established. Also, the existence and uniqueness of the pseudo- positive solution, the iterative sequence of the solution and an error estimation for the pseudo- positive solution are obtained. [Copyright &y& Elsevier]