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,
Stepan A. Tersian
Affiliations
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
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.
