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Lower and Upper Solutions for Even Order Boundary Value Problems

Author

Listed:
  • 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
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Alberto Cabada & Lucía López-Somoza, 2019. "Lower and Upper Solutions for Even Order Boundary Value Problems," Mathematics, MDPI, vol. 7(10), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:878-:d:269482
    as

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