Uniqueness and parameter dependence of positive solutions of fourth-order second-point nonhomogeneous BVPs
SHEN Wenguo1， SUN Jianren2， BAO Liqun3
1.Department of Basic Courses， Lanzhou Institute of Technology， Lanzhou 730050， China；2.College of Mechano-Electronic Engineering， Lanzhou Institute of Technology， Lanzhou 730050， China；3.College of Electronic and Information Engineering， Lanzhou Institute of Technology， Lanzhou 730050， China
Abstract：In this paper， by using the mixed monotone operator theory in cones， the fourth-order second-point nonhomogeneous boundary-value problem is investigated： x′′′′＋f(t，x)＝0，t∈，x＝α，x′＝β，x＝λ，x′＝－μ， where α〉0，β〉0，λ〉0，μ〉0， f(t，x)∈C([0,1]×[0，∞)，[0，∞)) is continuous and monotonically increasing for x. There exists 0≤θ〈1 such that f(t，kx)≥kθf(t，x)，t∈[0,1]，k∈[0,1]，x∈[0，∞). The existence and uniqueness of a positive solution and for the above problem is proved and the dependence of this solution on the parameters α，β，λ and μ is studied.
2021, Vol. 55 
