非线性非单调二元算子方程组的解及其应用

Solutions of Systems of Nonlinear Non-monotone Two Binary Operator Equations and Applications

利用非线性泛函分析中的锥理论和单调迭代的方法,研究了一类非线性非单调二元算子方程组的解的存在性,并给出了收敛于解的迭代序列,然后作为应用,得到了B anach空间中的一类非线性V olterra型积分方程组的解,改进了最近的许多结果.

In this paper, by using the cone theory and monotone iterative technique in nonlinear functional analysis, the existence of solutions for a class of systems of nonlinear non-mototone two binary operator equations is discussed. And the iterative sequences which converge to solutions are given. And then, as an application, the solutions for a class of systems of nonlinear integral equations of Volterra type in Banach spaces are obtained. The results presented here improve many recent results.