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Monotone Enclosure of Solutions for not Necessarily Convex Operator Equations and Applications to Mildly Nonlinear Boundary Value Problems
Author(s) -
Krätzschmar M.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860660704
Subject(s) - monotone polygon , mathematics , monotonic function , operator (biology) , nonlinear system , regular polygon , boundary value problem , enclosure , mathematical analysis , value (mathematics) , computer science , geometry , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , telecommunications , statistics
Monotone methods are applied to nonlinear operator equations in order to obtain sequences of upper and lower bounds for solutions. It is shown, that by relaxed regularity conditions to the ordering the sequences converge monotonically and superlinearly, too. The assumptions on the starting points are relaxed by consideration of different orderings in the range of the operator. The results are applied to mildly nonlinear boundary value problems.