TY - JOUR AU - Fonda, Alessandro AU - Toader, Rodica PY - 2011/04/23 Y2 - 2024/03/28 TI - Lower and upper solutions to semilinear boundary value problems: an abstract approach JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 38 IS - 1 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2011.024 SP - 59 - 93 AB - We provide an abstract setting for the theory of lower and upper solutions to some semilinear boundary value problems. In doing so, we need to introduce an abstract formulation of the Strong Maximum Principle. We thus obtain a general version of some existence results, both in the case where the lower and upper solutions are well-ordered, and in the case where they are not so. Applications are given, e.g. to boundary value problems associated to parabolic equations, as well as to elliptic equations. ER -