一类非线性发展方程解的存在性

Existence of Solution for a Class of Nonlinear Evolution Equations

利用Ｂｒｏｗｄｅｒ建立的单调型映射拓扑度理论和极大单调映射的特性，研究了一类非线性发展方程初值问题（Ｅ）ｄｕ（ｔ）ｄｔ＋Ａ（ｔ）ｕ（ｔ）＋Ｇ（ｔ）ｕ（ｔ）∈ｆ（ｔ）ｕ（０）＝ｕ０｛０≤ｔ≤Ｔ解的存在性，这里Ａ（ｔ）是多值极大单调映射，Ｇ（ｔ）是单值非单调映射·在Ｈｉｌｂｅｒｔ空间中，该结论是Ｈｉｒａｎｏ，Ａｈｍｅｄ等相应定理的发展和推广·

A class initial value problem of nonlinear evolution equation in Hilbert space was studied,where the nonlinear mapping is A+G . The existence of solution is proved by using Browders topological degree theory of monotone type mapping and property of maximal monotone mapping. A is the single monotone hemicontinuous operator and G is single nonmonotone operator in work of Hirano, Ahmed and the others is generalized to A is the multivalued maximal monotone mapping and G is the weaker single nonmonotone operator and A and G are allowed to depend on t .