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

Authors:
M. A. El-Gebeily;Donal O'Regan;J. J. Nieto
Affiliations:
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;Department of Mathematics, National University of Ireland, Galway, Ireland;Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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.