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Existence of positive solutions of a nonlinear differential equation for a thermostat model
Author(s) -
Shen Chunfang,
Zhou Hui,
Yang Liu
Publication year - 2018
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.5125
Subject(s) - thermostat , mathematics , nonlinear system , mathematical analysis , differential equation , boundary value problem , work (physics) , fixed point theorem , fixed point index , ordinary differential equation , order (exchange) , partial differential equation , thermodynamics , physics , finance , quantum mechanics , economics
We consider a second‐order nonlinear differential equation with various boundary conditions that arises as a model of a thermostat. By means of the Avery‐Peterson fixed‐point theorem, we establish the existence result of at least triple positive solutions. The results complete the previous work in the thermostat model in the way that the first‐order derivative is involved in the nonlinearity explicitly.