具有非线性内核和延迟参数的半线性偏函数积分微分方程在 $$\alpha $$-规范下的存在性结果、正则性和紧凑性特性

IF 0.9 Q2 MATHEMATICS
Boubacar Diao, Mamadou Sy
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引用次数: 0

摘要

在本文中,我们考虑的是一般巴拿赫空间中具有非线性核的有限延迟积分微分方程。假定非线性部分相对于线性部分在第二变量中的分数幂是连续的。我们利用半群理论证明了所谓温和解的局部存在性、初始数据的连续依赖性、炸裂现象、正则性和紧凑性。我们还提供了一个应用来说明我们的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Existence results, regularity and compactness properties, in the \(\alpha \)-norm, for semilinear partial functional integrodifferential equations with nonlinear Kernel and delay argument

In this paper, we consider a finite delay integro-differential equation with a nonlinear kernel in a general Banach space. The nonlinear part is assumed to be continuous with respect to a fractional power of the linear part in the second variable. We prove, using the semigroup theory, the local existence, continuous dependence of the initial data, the phenomena of blowing up, regularity, and compactness properties of the so-called mild solution. An application is provided to illustrate our results.

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来源期刊
Afrika Matematika
Afrika Matematika MATHEMATICS-
CiteScore
2.00
自引率
9.10%
发文量
96
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