scholarly journals Existence and uniqueness of positive solution for nonhomogeneous sublinear elliptic equations

2009 ◽  
Vol 358 (2) ◽  
pp. 307-319 ◽  
Author(s):  
Mohamed Benrhouma ◽  
Hichem Ounaies
Keyword(s):  
Positive Solution ◽  
Elliptic Equations ◽  
Existence And Uniqueness

Nonlocal problems arising from the birth-jump processes

2018 ◽  
Vol 149 (2) ◽  
pp. 447-469
Author(s):  
M. Delgado ◽  
A. Suárez ◽  
I. B. M. Duarte
Keyword(s):  
Positive Solution ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Solution Method ◽  
Eigenvalue Problems ◽  
Logistic Equation ◽  
Jump Processes ◽  
Nonlocal Problems

In this paper, we prove the existence and uniqueness of a positive solution for a nonlocal logistic equation arising from the birth-jump processes. For this, we establish a sub-super solution method for nonlocal elliptic equations, we perform a study of the eigenvalue problems associated with these equations and we apply these results to the nonlocal logistic equation.

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 .

Nonlinear Elliptic Equations in Strip-Like Domains

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Jaeyoung Byeon ◽  
Kazunaga Tanaka
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

AbstractWe study the existence of a positive solution of a nonlinear elliptic equationwhere k ≥ 2 and D is a bounded domain domain in R

scholarly journals EXISTENCE OF POSITIVE EVANESCENT SOLUTIONS TO SOME QUASILINEAR ELLIPTIC EQUATIONS

2008 ◽  
Vol 78 (1) ◽  
pp. 157-162 ◽  
Author(s):  
OCTAVIAN G. MUSTAFA
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Elliptic Equations ◽  
Exterior Domain ◽  
Quasilinear Elliptic Equations ◽  
Image Position ◽  
Quasilinear Elliptic

AbstractWe establish that the elliptic equation defined in an exterior domain of ℝn, n≥3, has a positive solution which decays to 0 as $\vert x\vert \rightarrow +\infty $ under quite general assumptions upon f and g.

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.

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