Banach空间中半线性发展方程的复合单调迭代技巧(英文)

Mixed Monotone Iterative Techniques for Semilinear Evolution Equations in Banach Spaces

本文对具有正则锥的序Banach空间中半线性发展方程,利用C0-半群理论和复合单调迭代技巧,构造出了抽象迭代格式,并建立了最大、最小(拟)解的存在性.

This note is concerned with initial value problems for semilinear evolution equations in an ordered Banach space with a regular cone.The abstract iterative schemes are constructed by combining the theory of postitive C 0-semigroups and the mixed monotone iterative techniques.Some existemce results on minimal and maximal (quasi-)solutions are established for abstract semilinear evolution equations with mixed monotone nonlinear terms.