关于m-增生型算子的扰动

On the Perturbation of Operators of m Accretive Type

给出了具有凝聚扰动的 ｍ耗散算子的一个不动点定理，利用这个定理得到了 ｍ增生型算子加凝聚扰动、紧扰动或有紧预解算子的零集存在性结论·在较弱的条件下，证明了 ｍ增生算子加紧扰动或有紧预解算子加连续有界扰动的满射性定理·这些结果都不需要空间一致凸的假设·给出了满射性定理在非线性偏微分方程解的存在性问题中应用的例子·

A fixed point theorem was given involving condensing perturbations of m dissipative operators. The theorem was applied to obtain the existence of zeros about operators of m accretive type with condensing perturbations,compact perturbations or compact resolvents. The surjectivity theorems were proved about m accretive operators: plus compact perturbations and plus continuous bounded perturbations with compact resolvents under weaker conditions. These results were obtained without the assumption that Banach space is uniformly convex. An example was given on the solution existence of the nonlinear partial differential equations by applying the surjectivity theorems.