Analysis of the Sign of the Solution for Certain Second-Order Periodic Boundary Value Problems with Piecewise Constant Arguments

Sebastián Buedo-Fernández, Daniel Cao Labora, Rosana Rodríguez-López and Stepan A. Tersian
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Sebastián Buedo-Fernández: Instituto de Matemáticas e Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Vida, 15782 Santiago de Compostela, Spain
Daniel Cao Labora: Instituto de Matemáticas e Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Vida, 15782 Santiago de Compostela, Spain
Rosana Rodríguez-López: Instituto de Matemáticas e Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Vida, 15782 Santiago de Compostela, Spain
Stepan A. Tersian: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 8., 1113 Sofia, Bulgaria

Mathematics, 2020, vol. 8, issue 11, 1-34

Abstract: We find sufficient conditions for the unique solution of certain second-order boundary value problems to have a constant sign. To this purpose, we use the expression in terms of a Green’s function of the unique solution for impulsive linear periodic boundary value problems associated with second-order differential equations with a functional dependence, which is a piecewise constant function. Our analysis lies in the study of the sign of the Green’s function.

Keywords: second-order differential equations; piecewise constant functional dependence; boundary value problems; Green’s function; comparison results; positive solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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