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Positive fixed points and fourth‐order equations
Author(s) -
Cid J. A.,
Franco D.,
Minhós F.
Publication year - 2009
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/bdn105
Subject(s) - mathematics , fixed point theorem , monotone polygon , fixed point , cone (formal languages) , section (typography) , nonlinear system , complement (music) , mathematical analysis , boundary value problem , order (exchange) , geometry , algorithm , biochemistry , chemistry , physics , finance , quantum mechanics , complementation , advertising , economics , business , gene , phenotype
This work presents sufficient conditions for the existence of at least one positive solution for a nonlinear fourth‐order beam equation under Lidstone boundary conditions. The main tool used is a fixed point theorem that essentially combines the monotone iterative technique with fixed point theorems of cone expansion or compression type. The last section contains two examples that complement some related results existent in the literature.