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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 4, 2001, pp. 1031–1054
DOI: 10.4171/ZAA/1058

Published online: 2001-12-31

Iteration Procedures of Shuttle Iteration Type in Continuous Non-Monotone Problems

D. Rachinskii[1]

(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