A unique positive solution for nth-order nonlinear impulsive singular integro-differential equations on unbounded domains in Banach spaces

2008 ◽  
Vol 203 (2) ◽  
pp. 649-659 ◽  
Author(s):  
Haijun Zhang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Banach Spaces ◽  
Unbounded Domains ◽  
Unique Positive Solution

scholarly journals Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift

2020 ◽  
Vol 25 (6) ◽  
pp. 1059-1078
Author(s):  
Kęstutis Kubilius
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Euler Scheme ◽  
Hurst Index ◽  
Unique Positive Solution ◽  
Backward Euler Scheme ◽  
Asymptotically Normal ◽  
Backward Euler ◽  
Locally Lipschitz ◽  
Strongly Consistent

Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.

scholarly journals Uniqueness of Successive Positive Solution for Nonlocal Singular Higher-Order Fractional Differential Equations Involving Arbitrary Derivatives

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Qiuyan Zhong ◽  
Xingqiu Zhang ◽  
Xinyi Lu ◽  
Zhengqing Fu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Higher Order ◽  
Unique Positive Solution ◽  
Mixed Monotone Operator ◽  
Iterative Schemes ◽  
Fractional Differential

In this article, by means of fixed point theorem on mixed monotone operator, we establish the uniqueness of positive solution for some nonlocal singular higher-order fractional differential equations involving arbitrary derivatives. We also give iterative schemes for approximating this unique positive solution.

scholarly journals Monotone iterative method for a class of nonlinear fractional differential equations on unbounded domains in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1331-1338 ◽  
Author(s):  
Lihong Zhang ◽  
Bashir Ahmad ◽  
Guotao Wang
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Nonnegative Solution ◽  
Unbounded Domains ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential ◽  
Infinite Intervals

In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone iterative technique. An example is given for the illustration of main results.

scholarly journals Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Tsing-San Hsu
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Exterior Domain ◽  
Unbounded Domains ◽  
Multiple Positive Solutions ◽  
Entire Space ◽  
Unique Positive Solution ◽  
Strip Domain ◽  
Unbounded Cylinder

We will show that under suitable conditions onfandh, there exists a positive numberλ∗such that the nonhomogeneous elliptic equation−Δu+u=λ(f(x,u)+h(x))inΩ,u∈H01(Ω),N≥2, has at least two positive solutions ifλ∈(0,λ∗), a unique positive solution ifλ=λ∗, and no positive solution ifλ>λ∗, whereΩis the entire space or an exterior domain or an unbounded cylinder domain or the complement in a strip domain of a bounded domain. We also obtain some properties of the set of solutions.

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