Lower and upper solutions to semilinear boundary value problems: an abstract approach

Alessandro Fonda, Rodica Toader

Abstract


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.

Keywords


Lower and upper solutions; maximum principle; semilinear equations; parabolic and elliptic problems

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