Lower and upper solutions to semilinear boundary value problems: an abstract approach
Keywords
Lower and upper solutions, maximum principle, semilinear equations, parabolic and elliptic problemsAbstract
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.Downloads
Published
2011-04-23
How to Cite
1.
FONDA, Alessandro and TOADER, Rodica. Lower and upper solutions to semilinear boundary value problems: an abstract approach. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 38, no. 1, pp. 59 - 93. [Accessed 28 March 2024].
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