Uniqueness and properties of positive solutions for infinite-point fractional differential equation with p-Laplacian 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 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.
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ISRP Style
Li Wang, Chengbo Zhai, Uniqueness and properties of positive solutions for infinite-point fractional differential equation with p-Laplacian and a parameter, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5156--5164
AMA Style
Wang Li, Zhai Chengbo, Uniqueness and properties of positive solutions for infinite-point fractional differential equation with p-Laplacian and a parameter. J. Nonlinear Sci. Appl. (2017); 10(10):5156--5164
Chicago/Turabian Style
Wang, Li, Zhai, Chengbo. "Uniqueness and properties of positive solutions for infinite-point fractional differential equation with p-Laplacian and a parameter." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5156--5164
Keywords
- Uniqueness
- positive solution
- \(p\)-Laplacian
- infinite-point fractional differential equation
- mixed monotone operator
MSC
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