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Applications of Schauder's fixed point theorem to singular differential equations
Author(s) -
Chu Jifeng,
Torres Pedro J.
Publication year - 2007
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/bdm040
Subject(s) - mathematics , fixed point theorem , schauder fixed point theorem , gravitational singularity , mathematical analysis , picard–lindelöf theorem , order (exchange) , differential equation , pure mathematics , economics , finance
In this paper, we study the existence of positive periodic solutions to second‐order singular differential equations. The proof relies on Schauder's fixed point theorem. Our results show that in some situations weak singularities can help create periodic solutions, as pointed out by Torres [ J. Differential Equations 232 (2007) 277–284].