Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Existence, Uniqueness and Input-To-State Stability of Ground-State Stationary Strong Solution of a Single-Species Model via Mountain Pass Lemma

Version 1 : Received: 12 September 2020 / Approved: 13 September 2020 / Online: 13 September 2020 (12:26:12 CEST)

How to cite: Rao, R. Existence, Uniqueness and Input-To-State Stability of Ground-State Stationary Strong Solution of a Single-Species Model via Mountain Pass Lemma. Preprints 2020, 2020090286 (doi: 10.20944/preprints202009.0286.v1). Rao, R. Existence, Uniqueness and Input-To-State Stability of Ground-State Stationary Strong Solution of a Single-Species Model via Mountain Pass Lemma. Preprints 2020, 2020090286 (doi: 10.20944/preprints202009.0286.v1).

Abstract

In this paper, the authors employ Mountain Pass Lemma, the method of weak solution regularization and Lyapunov function method to derive the unique existence of globally exponential stable positive stationary solution of a single-species model with diffusion and delayed feedback. The obtained stability criterion illuminates that under some suitable conditions, a certain internal competition is conducive to the overall stability of the population, and a certain amount of family planning is conducive to the overall stability of the population. A numerical example and three tables show the effectiveness of the proposed methods.

Subject Areas

strong solution; regularity of weak Solutions; a single-species ecosystem; Lyapunov function; Mountain Pass Lemma; unique existence

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.