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2022 Positive solutions of Neumann boundary value problems and applications to logistic type population models
Ziyi Cai, Kunquan Lan
Topol. Methods Nonlinear Anal. 59(1): 35-52 (2022). DOI: 10.12775/TMNA.2021.013

Abstract

We study the existence of nonzero nonnegative or strictly positive solutions of second order Neumann boundary value problems with nonlinearities which are allowed to take negative values via a recently established fixed point theorem for $r$-nowhere normal-outward maps in Banach spaces. As applications, we obtain results on the existence of strictly positive solutions for some models of population inhabiting one dimensional heterogeneous environments with perfect barriers, where the local rate of change in the population density changes sign.

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Ziyi Cai. Kunquan Lan. "Positive solutions of Neumann boundary value problems and applications to logistic type population models." Topol. Methods Nonlinear Anal. 59 (1) 35 - 52, 2022. https://doi.org/10.12775/TMNA.2021.013

Information

Published: 2022
First available in Project Euclid: 23 March 2022

Digital Object Identifier: 10.12775/TMNA.2021.013

Keywords: $r$-nowhere normal-outward map , Neumann boundary value problem , one dimensional population model , strictly positive solution

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.59 • No. 1 • 2022
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