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

作者：El Gebeily M A^*; O'Regan Donal; Nieto J J

来源：Journal of Computational and Applied Mathematics, 2010, 233(9): 2395-2404.

DOI：10.1016/j.cam.2009.10.024

• Nonlinear operators
• Monotone operators
• Existence
• Partially ordered spaces
• Cauchy problem

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.

• 出版日期2010-3-1
• 单位中国石油大学（北京）