一类非单调算子方程解的存在性及应用

On Solution Existence and Applications of a Class of Nonmonotone Operator Equation

在实Banach空间中,利用锥理论和单调迭代方法,推广了A(x,y)+Mx中混合单调条件,用A(x,y)+Tx来代替以往的混合单调性.给出了一类非单调算子方程x=A(x,x)解的存在性定理,并对脉冲微分方程初值问题进行了讨论.

By using cone theorem and monotone iterative method, the mixed monotone condition in A （x,y） ＋Mx in Banach spaces is extended. The traditional mixed monotonicity is replaced by A（x,y）＋Tx. Then the existence of solutions for a kind of nonmonotonic operator equation is given and the initial value problems for impulsive differential equations are discussed.