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Homoclinic solutions for nonlinear general fourth‐order differential equations
Author(s) -
Carrasco Hugo,
Minhós Feliz
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4426
Subject(s) - mathematics , homoclinic orbit , nonlinear system , mathematical analysis , fixed point theorem , differential equation , schauder fixed point theorem , ordinary differential equation , partial differential equation , order (exchange) , operator (biology) , integral equation , picard–lindelöf theorem , bifurcation , biochemistry , chemistry , physics , finance , repressor , quantum mechanics , transcription factor , economics , gene
This work provides sufficient conditions for the existence of homoclinic solutions of fourth‐order nonlinear ordinary differential equations. Using Green's functions, we formulate a new modified integral equation that is equivalent to the original nonlinear equation. In an adequate function space, the corresponding nonlinear integral operator is compact, and it is proved an existence result by Schauder's fixed point theorem. Copyright © 2017 John Wiley & Sons, Ltd.