Positive solutions for the periodic-parabolic problem with large diffusion

Mingming Fan; Jianwen Sun; Mingming Fan; Jianwen Sun

doi:10.3934/nhm.2024049

Networks and Heterogeneous Media

2024, Volume 19, Issue 3: 1116-1132. doi: 10.3934/nhm.2024049

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Positive solutions for the periodic-parabolic problem with large diffusion

Mingming Fan ,
Jianwen Sun ^,

School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Received: 10 August 2024 Revised: 26 September 2024 Accepted: 09 October 2024 Published: 12 October 2024

In this paper, we study the positive solutions of the periodic-parabolic logistic equation with indefinite weight function and nonhomogeneous diffusion coefficient. By employing sufficient conditions to guarantee negative principal eigenvalue, we obtain the existence, uniqueness, and stability of the positive periodic solutions. Moreover, we prove that the positive periodic solution tends to the unique positive solution of the corresponding non-autonomous logistic equation when the diffusion rate is large.
- logistic equation,
- periodic-parabolic,
- periodic solution
Citation: Mingming Fan, Jianwen Sun. Positive solutions for the periodic-parabolic problem with large diffusion[J]. Networks and Heterogeneous Media, 2024, 19(3): 1116-1132. doi: 10.3934/nhm.2024049

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Abstract

In this paper, we study the positive solutions of the periodic-parabolic logistic equation with indefinite weight function and nonhomogeneous diffusion coefficient. By employing sufficient conditions to guarantee negative principal eigenvalue, we obtain the existence, uniqueness, and stability of the positive periodic solutions. Moreover, we prove that the positive periodic solution tends to the unique positive solution of the corresponding non-autonomous logistic equation when the diffusion rate is large.

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