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.
General
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