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

Ruofeng Rao

doi:10.20944/preprints202009.0286.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

Computer Science and Mathematics, Applied Mathematics

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

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