Existence and Multiplicity Results for Systems of First-Order Differential Equations via the Method of Solution-Regions-Reference-Cited by-同舟云学术

Existence and Multiplicity Results for Systems of First-Order Differential Equations via the Method of Solution-Regions

Published:2018-02-07 Issue:3 Volume:18 Page:469-485
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Frigon Marlène¹

Affiliation:

1. Department of Mathematics and Statistic , University of Montréal , Montréal , QC, H3C 3J7 , Canada

Abstract

Abstract In this paper, we establish existence and multiplicity results for systems of first-order differential equations. To this end, we introduce the method of solution-regions. It generalizes the method of upper and lower solutions and the method of solution-tubes. Our results can also be seen as viability results since we obtain solutions remaining in suitable regions. We give conditions insuring the existence of at least three viable solutions of a system of first-order differential equations. Many examples are presented to show that a large variety of sets can be solution-regions.

Funder

Natural Sciences and Engineering Research Council of Canada

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2017-6049/pdf

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