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Minimal and maximal solutions to second‐order boundary value problems with state‐dependent deviating arguments
Author(s) -
Figueroa Rubén,
Pouso Rodrigo López
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq091
Subject(s) - mathematics , upper and lower bounds , boundary value problem , order (exchange) , value (mathematics) , state (computer science) , set (abstract data type) , derivative (finance) , mathematical analysis , statistics , algorithm , finance , computer science , financial economics , economics , programming language
We prove the existence of solutions between given lower and upper solutions for second‐order boundary value problems with deviating arguments, and we show that the set of those solutions has minimal and maximal elements, but not necessarily a least or a greatest one. We consider deviating functions which depend on the unknown solution and its derivative. Some sufficient conditions for having lower and upper solutions are also provided.