High order Boundary Value Problems: Existence, localization and multiplicity results - Fialho, João (2015)
The motto for all the results presented in this book is the lower and upper solution method. In short, this method can guarantee not only the existence of a solution for a given boundary value problem but also the location of the solution in a strip defined by the lower and the upper solutions. Therefore, the challenge of finding a solution for a boundary value problem is replaced by the search of two functions (well-ordered, in reversed order or non-ordered) satisfying adequate differential inequalities and boundary conditions. The freedom to choose such functions is at the same time its weakness: lower and upper solutions must be defined and exhibited.