We suggest and study iteration procedures converging from below and above to robust stable solutions and to robust stable continuous branches of solutions for quasilinear boundary-value problems with continuous non-monotone non-linearities. The iterations are constructed by modifications of the shuttle iteration method, which is used in problems with monotone operators leaving invariant a cone interval.
Cite this article
D. Rachinskii, Iteration Procedures of Shuttle Iteration Type in Continuous Non-Monotone Problems. Z. Anal. Anwend. 20 (2001), no. 4, pp. 1031–1054DOI 10.4171/ZAA/1058