Clément, Philippe; Sweers, Guido Getting a solution between sub- and supersolutions without monotone iteration. (English) Zbl 0687.35037 Rend. Ist. Mat. Univ. Trieste 19, No. 2, 189-194 (1987). 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. Cited in 1 ReviewCited in 13 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 47H10 Fixed-point theorems 35B50 Maximum principles in context of PDEs Keywords:continuous nonlinearity; semilinear elliptic problem; Schauder fixed point theorem; sub- and supersolution PDFBibTeX XMLCite \textit{P. Clément} and \textit{G. Sweers}, Rend. Ist. Mat. Univ. Trieste 19, No. 2, 189--194 (1987; Zbl 0687.35037)