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Getting a solution between sub- and supersolutions without monotone iteration. (English) Zbl 0687.35037

Summary: If there exist a sub- and a supersolution for a semilinear elliptic problem, then one can show the existence of a solution by a monotone iteration scheme. In order to do this one needs more than continuity of the right-hand side.
In this note the Schauder fixed point theorem and a version of the strong maximum principle is used to get existence of a solution with only continuity of the right-hand side under the existence of a weak sub- and supersolution.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
47H10 Fixed-point theorems
35B50 Maximum principles in context of PDEs
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