Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations

Feliz Minhós () and Gracino Rodrigues
Additional contact information
Feliz Minhós: Department of Mathematics, School of Science and Technology, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Gracino Rodrigues: Center for Research in Mathematics and Applications, Institute for Advanced Studies and Research, University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal

Mathematics, 2023, vol. 11, issue 17, 1-19

Abstract: This paper deals with two types of systems of second-order differential equations with parameters: coupled systems with the boundary conditions of the Sturm–Liouville type and classical systems with Dirichlet boundary conditions. We discuss an Ambosetti–Prodi alternative for each system. For the first type of system, we present sufficient conditions for the existence and non-existence of its solutions, and for the second type of system, we present sufficient conditions for the existence and non-existence of a multiplicity of its solutions. Our arguments apply the lower and upper solutions method together with the properties of the Leary–Schauder topological degree theory. To the best of our knowledge, the present study is the first time that the Ambrosetti–Prodi alternative has been obtained for such systems with different parameters.

Keywords: coupled systems; lower and upper solutions; Nagumo condition; degree theory; Ambrosetti–Prodi problems; Lotka–Volterra systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/17/3645/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/17/3645/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:17:p:3645-:d:1223538

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().