MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES

• 作者: 王志成 王良龙
• 来源期刊: 微分方程年刊：英文版
• 学科: 数学
• 关键词: 迭代法 半线性发展方程 混合 初值问题 巴拿赫空间 半群
• 年，卷（期）: 2004,（3）
• 页码范围: 283-301
• 页数: 19页
• 分类号: O177.2

摘要

This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.