A note on the Maximum Principle and the Iteration Method for elliptic\n equations

2021/06/23 by Jean C. Cortissoz, Cortissoz, Jean, Jonatán Torres-Orozco +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2106.12650

openalex publication_date 2021/06/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We use an iteration procedure propped up by a a classical form of the maximum\nprinciple to show the existence of solutions to a nonlinear Poisson equation\nwith Dirichlet boundary conditions. These methods can be applied to the case of\nspecial unbounded domains, and can be adapted to show the existence of\nnontrivial solutions to systems, which we show via some examples.\n

Citations

• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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