Lower and Upper Solutions for Even Order Boundary Value Problems

Alberto Cabada and Lucía López-Somoza
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Alberto Cabada: Departamento de Estatística, Análise Matemática e Optimización Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782 Galicia, Spain
Lucía López-Somoza: Departamento de Estatística, Análise Matemática e Optimización Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782 Galicia, Spain

Mathematics, 2019, vol. 7, issue 10, 1-20

Abstract: In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions of a considered problem could imply the existence of solution of another one with different boundary conditions. We consider Neumann, Dirichlet, mixed and periodic boundary conditions.

Keywords: Green’s functions; two-point boundary conditions; lower and upper solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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