Existence of periodic solutions in abstract semilinear equations and applications to biological models
Existence of periodic solutions in abstract semilinear equations and applications to biological models
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DOI：
10.1016/j.jde.2020.07.014
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发表时间：
2020-12
影响因子：
2.4
通讯作者：
Qiuyi Su;S. Ruan
中科院分区：
文献类型：
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作者：
Qiuyi Su;S. Ruan
在这篇文章中，我们研究了一类抽象半线性方程的温和周期解的存在性，这类方程包括时滞微分方程、一阶双曲型偏微分方程及反应扩散方程。在对线性算子和非齐次函数的不同假设下，得到了抽象半线性方程存在温和周期解的充分条件。当线性算子生成的半群不是紧的时，利用Banach不动点定理；当线性算子生成的半群是紧的时，利用Schauder不动点定理。在应用中，我们将主要结果应用于时滞红细胞模型、具有周期收获的年龄结构模型和具有周期系数的扩散Logistic方程，建立了周期解的存在性。
In this paper, we study the existence of mild periodic solutions of abstract semilinear equations in a setting that includes several other types of equations such as delay differential equations, first-order hyperbolic partial differential equations, and reaction-diffusion equations. Under different assumptions on the linear operator and the nonhomogeneous function, sufficient conditions are derived to ensure the existence of mild periodic solutions in the abstract semilinear equations. When the semigroup generated by the linear operator is not compact, Banach fixed point theorem is used whereas when the semigroup generated by the linear operator is compact, Schauder fixed point theorem is employed. In applications, we apply the main results to establish the existence of periodic solutions in delayed red-blood cell models, age-structured models with periodic harvesting, and the diffusive logistic equation with periodic coefficients.