scholarly journals Further study on existence and uniqueness of positive solution for tensor equations

2022 ◽  
Vol 124 ◽  
pp. 107686
Author(s):  
Lixia Liu ◽  
Xinyi Li ◽  
Sanyang Liu
Keyword(s):  
Positive Solution ◽  
Existence And Uniqueness

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

scholarly journals Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Imed Bachar ◽  
Habib Mâagli
Keyword(s):  
Dirichlet Problem ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Nonlinear Effects ◽  
Weight Functions ◽  
Global Behavior ◽  
Bounded Domains ◽  
Euclidian Distance ◽  
Nonnegative Weight

We prove the existence and uniqueness of a positive continuous solution to the following singular semilinear fractional Dirichlet problem(-Δ)α/2u=a1(x)uσ1+a2(x)uσ2, in D  limx→z∈∂D(δ(x))1-(α/2)u(x)=0,where0<α<2, σ1,  σ2∈(-1,1), Dis a boundedC1,1-domain inℝn,n≥2,andδ(x)denotes the Euclidian distance fromxto the boundary ofD.The nonnegative weight functionsa1,  a2are required to satisfy certain hypotheses related to the Karamata class. We also investigate the global behavior of such solution.

scholarly journals The Unique Positive Solution for Singular Hadamard Fractional Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Jinxiu Mao ◽  
Zengqin Zhao ◽  
Chenguang Wang
Keyword(s):  
Exact Solution ◽  
Convergence Rate ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Approximation Error ◽  
Iterative Solution ◽  
Unique Positive Solution ◽  
Fractional Boundary Value Problems

In this paper, we investigate singular Hadamard fractional boundary value problems. The existence and uniqueness of the exact iterative solution are established only by using an iterative algorithm. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have also been derived.

scholarly journals Existence and Uniqueness of Positive Solution for Discrete Multipoint Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huili Ma ◽  
Huifang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ2u(t-1)=f(t,   u(t))+g(t,   u(t)),  t∈Z1,  T, subject to boundary conditions either u(0)-βΔu(0)=0, u(T+1)=αu(η) or Δu(0)=0, u(T+1)=αu(η), where 0<α<1,   β>0,  and   η∈Z2,T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.

scholarly journals Existence and Uniqueness of Positive Solution for Singular BVPs on Time Scales

2009 ◽  
Vol 2009 (1) ◽  
pp. 728484 ◽  
Author(s):  
Ana Gómez González ◽  
Victoria Otero-Espinar
Keyword(s):  
Positive Solution ◽  
Time Scales ◽  
Existence And Uniqueness

scholarly journals Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ramzi S. Alsaedi
Keyword(s):  
Continuous Function ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Global Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution to the following fourth-order value problem:u(4)(x)=a(x)uσ(x),x∈(0,1)with the boundary conditionsu(0)=u(1)=u'(0)=u'(1)=0, whereσ∈(-1,1)andais a nonnegative continuous function on (0, 1) that may be singular atx=0orx=1. We also give the global behavior of such a solution.

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