摘要
混合单调算子是一类重要的非线性算子,它广泛出现在非线性微分方程与积分方程的研究中.一般来说,在半序Banach空间的研究中此项研究常要求算子有紧性连续性或凹凸性.最近杜心欣对一类混合单调算子证明了正不动点存在唯一的一些结果.本文我们跟随杜心欣的文章获得了正三重不动点的存在性,唯一性,这里假定所论算子是e-凹凸的而相应Banach空间是由锥定序的,无需假定算子是紧的或连续的.作为应用,我们对一分数阶微分方程边值问题的正解给出若干结果.
Mixed monotone operator is an important nonlinear operator.It exists extensively in the research of nonlinear differential and integral equations.Generally,the research of mixed monotone operators in partially ordered Banach spaces requires compactness,continuity or concavity-convexity of the operators.Newly,Xinshing Du proved some results on the existence and uniqueness of positive fixed points for a class of mixed monotone operators.In this paper,following the paper of Xinshing we get the existence and uniqueness of positive tripled fixed points of e-concave-convex mixed monotone operators in Banach spaces partially ordered by a cone without assuming the operator to be compact or continuous.As an application,we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for a fractional differential equation boundary value problem.
出处
《南京大学学报（数学半年刊）》
CAS
2014年第2期174-186,共13页
Journal of Nanjing University(Mathematical Biquarterly)
关键词
三重不动点
混合单调算子
正规锥
正解
分数阶微分方程
tripled fixed point
mixed monotone operator
normal cone
positive solution
fractional differential equation
