半線性分?jǐn)?shù)次發(fā)展方程的非局部Cauchy問題

肖 飛

半線性分?jǐn)?shù)次發(fā)展方程的非局部Cauchy問題

肖 飛

(井岡山大學(xué)數(shù)理學(xué)院，江西 吉安 343000)

針對一種定義在Banach空間上的帶有非局部條件的半線性分?jǐn)?shù)次發(fā)展方程的Cauchy問題，利用krasnoselkii不動點(diǎn)定理，得到了mild解的存在性定理。最后，應(yīng)用我們給出的定理證明了一類微分方程mild解的存在性。

分?jǐn)?shù)次發(fā)展方程；解；非局部條件

0 引言和預(yù)備知識

1 主要結(jié)論

定理 1 假設(shè)條件(H1)-(H3)成立，且滿足：

則有

現(xiàn)在假設(shè)：

于是

其中

根據(jù)條件(H2)，有

根據(jù)條件(H4)，可得

2 應(yīng)用

考慮如下的分?jǐn)?shù)次發(fā)展方程：

則根據(jù)定理3可知方程(3.1)存在mild解。

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The Cauchy Problem of Similinear Fractional Evolution Equation with Nonlocal condition

XIAO Fei

(School of Mathmatics Science& Physics, Jinggangshan University, Ji’an, Jiangxi 343000, China)

We discuss in this paper the existence and uniqueness of mild solution to the Cau-chy problem for the semilinear fractional evolution equations with nonlocal conditions in a Banach spaces. New results are given. Finally, we give an example to illustrate our main result.

fractional evolution equation; mild solution; nonlocal condition

O 175.6

A

10.3969/j.issn.1674-8085.2020.04.001

1674-8085(2020)04-0001-05

2019-10-19；

2020-04-10

國家自然科學(xué)基金項目(11761032)

肖 飛(1981-)，男，江西吉安人，講師，博士，主要從事泛函分析、微分幾何研究(E-mail: xiaofeishuxue@126.com).