一类半线性分数阶发展包含初值问题解的存在性

Existence of solutions for a class of semilinear fractional evolution inclusions initial value problems

通过引入非紧性测度的一种新定义,在线性算子半群非紧非等度连续的情形下获得了解算子的紧性,进而讨论了一类半线性分数阶发展包含初值问题局部mild解、饱和mild解和整体mild解的存在性,改进和推广了一些发展包含解的存在性结果。

By introducing a new definition of the measure of non-compactness,the compactness of the solution operator is obtained when the linear operator semigroup is noncompact and non-equicontinuous.Then the existence of local mild solutions,saturated mild solutions and global mild solutions for a class of semilinear fractional evolution problems with initial value is discussed.Some existence results of evolution inclusion solutions are improved and generalized.