Open AccessThe existence of solutions and positive solution of a first - order differential system with initial and multi-point boundary conditions
Author(s) -
Nguyen Long Thanh,
L. T. Minh,
Le Ngoc Thi
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2105629l
Subject(s) - mathematics , fixed point theorem , multiplicity (mathematics) , picard–lindelöf theorem , mathematical analysis , fixed point , banach fixed point theorem , contraction principle , boundary value problem , brouwer fixed point theorem , nonlinear system , order (exchange) , kakutani fixed point theorem , contraction mapping , schauder fixed point theorem , physics , finance , quantum mechanics , economics
In this paper, we consider a nonlinear differential system with initial and multi - point boundary conditions. The existence of solutions is proved by using the Banach contraction principle or the Krasnoselskii?s fixed point theorem. Furthermore, the existence of positive solutions is also obtained by applying the Guo-Krasnoselskii?s fixed point theorem in cones. As a consequence of the Guo-Krasnosellskii?s fixed point theorem, the multiplicity of positive solutions is established.