First order differential systems with a nonlinear boundary condition via the method of solution-regions

Marlène Frigon; Marcos Tella; F Adrián F Tojo

doi:10.1186/s13661-021-01495-9

First order differential systems with a nonlinear boundary condition via the method of solution-regions

Bound Value Probl. 2021;2021(1):19. doi: 10.1186/s13661-021-01495-9. Epub 2021 Feb 19.

Authors

Marlène Frigon¹, Marcos Tella², F Adrián F Tojo²

Affiliations

¹ Département de mathématiques et de statistique, Université de Montréal, Montreal, Canada.
² Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain.

Abstract

In this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear case.

Keywords: Existence results; Nonlinear boundary conditions; Solution regions; Upper and lower solutions.