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A monotone iterative technique for stationary and time dependent problems in Banach spaces

✍ Scribed by M.A. El-Gebeily; Donal O’Regan; J.J. Nieto

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
575 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

An abstract monotone iterative method is developed for operators between partially ordered Banach spaces for the nonlinear problem Lu = Nu and the nonlinear time dependent problem u = (L + N)u. Under appropriate assumptions on L and N we obtain maximal and minimal solutions as limits of monotone sequences of solutions of linear problems. The results are illustrated by means of concrete examples.

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