Uniqueness and properties of positive solutions for infinitepoint fractional differential equation with pLaplacian and a parameter

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Authors
Li Wang
 School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P. R. China.
Chengbo Zhai
 School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P. R. China.
Abstract
Using new methods for dealing with an infinitepoint fractional differential equation with pLaplacian 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.
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ISRP Style
Li Wang, Chengbo Zhai, Uniqueness and properties of positive solutions for infinitepoint fractional differential equation with pLaplacian and a parameter, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 51565164
AMA Style
Wang Li, Zhai Chengbo, Uniqueness and properties of positive solutions for infinitepoint fractional differential equation with pLaplacian and a parameter. J. Nonlinear Sci. Appl. (2017); 10(10):51565164
Chicago/Turabian Style
Wang, Li, Zhai, Chengbo. "Uniqueness and properties of positive solutions for infinitepoint fractional differential equation with pLaplacian and a parameter." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 51565164
Keywords
 Uniqueness
 positive solution
 \(p\)Laplacian
 infinitepoint fractional differential equation
 mixed monotone operator
MSC
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