TY - JOUR AU - Wang, Li AU - Zhai, Chengbo PY - 2017 TI - Uniqueness and properties of positive solutions for infinite-point fractional differential equation with p-Laplacian and a parameter JO - Journal of Nonlinear Sciences and Applications SP - 5156--5164 VL - 10 IS - 10 AB - Using new methods for dealing with an infinite-point fractional differential equation with p-Laplacian and a parameter, we study the existence of unique positive solution for any given positive parameter \(\lambda\), and then give some clear properties of positive solutions which depend on the parameter \(\lambda>0\), that is, the positive solution \(u_\lambda^{*}\) is continuous, strictly increasing in \(\lambda\) and \(\lim_{\lambda\rightarrow +\infty}\|u_\lambda^*\|=+\infty,\lim_{\lambda\rightarrow 0^+}\|u_\lambda^*\|=0.\) Our analysis relies on some new theorems for operator equations \(A(x,x)=x\) and \(A(x,x)=\lambda x\), where \(A\) is a mixed monotone operator. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.10.03 DO - 10.22436/jnsa.010.10.03 ID - Wang2017 ER -