Coupled systems with Ambrosetti-Prodi-type differential equations-Reference-Cited by-同舟云学术

Coupled systems with Ambrosetti-Prodi-type differential equations

Published:2023 Issue:8 Volume:8 Page:19049-19066
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Minhós F.¹²,Carapau F.¹²,Rodrigues G.¹²³

Affiliation:

1. Department of Mathematics, School of Science and Technology, Institute for Advanced Studies and Research (IIFA), University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal

2. Center for Research in Mathematics and Applications (CIMA), Institute for Advanced Studies and Research (IIFA), University of Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal

3. Coordination of Degree in Mathematics, Campus Maceió, Federal Institute of Education, Science and Technology of Alagoas (IFAL), R. Mizael Domingues, 530-Centro, Maceió-AL, 57020-600, Brazil

Abstract

<abstract><p>In this paper, we consider some boundary value problems composed by coupled systems of second-order differential equations with full nonlinearities and general functional boundary conditions verifying some monotone assumptions. The arguments apply the lower and upper solutions method, and defining an adequate auxiliary, homotopic, and truncated problem, it is possible to apply topological degree theory as the tool to prove the existence of solution. In short, it is proved that for the parameter values such that there are lower and upper solutions, then there is also, at least, a solution and this solution is localized in a strip bounded by lower and upper solutions. As far as we know, it is the first paper where Ambrosetti-Prodi differential equations are considered in couple systems with different parameters.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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