Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2001-12-31
Iteration Procedures of Shuttle Iteration Type in Continuous Non-Monotone ProblemsD. Rachinskii (1) Russian Academy of Sciences, Moscow, Russian Federation
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.
Keywords: Cone semiordering, monotone operator, robust stable solution, continuous branch of solutions, second order elliptic operator
Rachinskii D.: Iteration Procedures of Shuttle Iteration Type in Continuous Non-Monotone Problems. Z. Anal. Anwend. 20 (2001), 1031-1054. doi: 10.4171/ZAA/1058