Hilbert空间中一类非线性算子方程解

Solutions for a class of nonlinear operator equations in Hilbert spaces

利用半闭1-集压缩算子的不动点指数方法,在不同边界条件下研究了实Hilbert空间中非线性算子方程Ax=μx-p(μ≥1)的解的存在性问题,得到了若干新的结果,并给出了主要定理的一个应用。

Using the fixed point index of semi-closed 1-set-contractive operators,the existence of solutions for a class of nonlinear operator equations Ax = μx- p（ μ≥1） was studied,and some new results were obtained. Meanwhile,an example is also given to show the application of one of the main theorems.