一类涉及时滞的非局部半线性方程的存在性和稳定性结果

Pub Date : 2023-01-01 DOI:10.4064/ap220912-5-4

Nguyễn Như Quân

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引用次数: 0

摘要

．研究了一类有限时滞非局部半线性方程温和解的存在性和弱稳定性。基于局部估计和不动点论证，我们证明了非线性为超线性或次线性问题的温和解的整体存在性，且不存在初始数据或系数的小条件。然后利用一个特殊的非紧性度量，给出了保证温和解弱稳定性的几个充分条件。

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Existence and stability results for a class of nonlocal semilinear equations involving delays

. We investigate the existence and weak stability of mild solutions for a class of nonlocal semilinear equations involving ﬁnite delays. Based on local estimates and ﬁxed point arguments, we prove the global existence of mild solutions to problems in which the nonlinearity is superlinear or sublinear without the smallness condition on initial data or on the coeﬃcients. Then by using a special measure of noncompactness, we show some suﬃcient conditions ensuring the weak stability of mild solutions.

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