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A monotone iterative technique for stationary and time dependent problems in Banach spaces |
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| Authors: | M.A. El-Gebeily,Donal O&rsquo Regan |
| Affiliation: | a Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia b Department of Mathematics, National University of Ireland, Galway, Ireland c Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain |
| 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. |
| Keywords: | 46N10 41A65 47J05 47J25 |
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