MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES  

作　　者：王良龙 王志成 

机构地区：[1]Dept,of Math.,University of Science and Technology of China,Hefei 230026 [2]Dept.of Appl.Math.,Hunan University,Changsha 410082his 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.

出　　处：《Annals of Differential Equations》2004年第3期283-301,共19页微分方程年刊（英文版）

基　　金：This work was supported by grants from NNSF of China(No:10271044);Scientific Research Fund of Educational Department of Anhui Province(NSF2003KJ005zd);Teaching Research Fund of Educational Department of Anhui Province(JYXM2003108).

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.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.

关 键 词：normal or regular cone positive Co-semigroup mixed monotone technique mixed monotonicity semilinear evolution equations coupled lower and upper quasi-solutions 

分 类 号：O177.2[理学—数学]