Existence and global asymptotic behavior of positive solutions for superlinear fractional dirichlet problems on the half-line

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Imed Bachar ◽  
Habib Mâagli
Keyword(s):  
Asymptotic Behavior ◽  
Green Function ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Half Line ◽  
Dirichlet Problems ◽  
The Green Function

AbstractUsing estimates on the Green function and a perturbation argument, we prove the existence and uniqueness of a positive continuous solution to problem:

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 Weighted fourth order elliptic problems in the unit ball

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zongming Guo ◽  
Fangshu Wan
Keyword(s):  
Asymptotic Behavior ◽  
Singular Point ◽  
Unit Ball ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Uniqueness Results ◽  
Positive Radial Solutions

<p style='text-indent:20px;'>Existence and uniqueness of positive radial solutions of some weighted fourth order elliptic Navier and Dirichlet problems in the unit ball <inline-formula><tex-math id="M1">\begin{document}$ B $\end{document}</tex-math></inline-formula> are studied. The weights can be singular at <inline-formula><tex-math id="M2">\begin{document}$ x = 0 \in B $\end{document}</tex-math></inline-formula>. Existence of positive radial solutions of the problems is obtained via variational methods in the weighted Sobolev spaces. To obtain the uniqueness results, we need to know exactly the asymptotic behavior of the solutions at the singular point <inline-formula><tex-math id="M3">\begin{document}$ x = 0 $\end{document}</tex-math></inline-formula>.</p>

scholarly journals A biharmonic equation with singular nonlinearity

2011 ◽  
Vol 55 (1) ◽  
pp. 155-166 ◽  
Author(s):  
Marius Ghergu
Keyword(s):  
Green Function ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Biharmonic Equation ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Biharmonic Operator ◽  
The Green Function ◽  
Uniqueness Of A Solution

AbstractWe study the biharmonic equation Δ2u=u−α, 0 < α < 1, in a smooth and bounded domain Ω ⊂ ℝn,n≥ 2, subject to Dirichlet boundary conditions. Under some suitable assumptions on Ω related to the positivity of the Green function for the biharmonic operator, we prove the existence and uniqueness of a solution.

ESTIMATES ON THE GREEN FUNCTION AND EXISTENCE OF POSITIVE SOLUTIONS FOR SOME NONLINEAR POLYHARMONIC PROBLEMS OUTSIDE THE UNIT BALL

2008 ◽  
Vol 06 (02) ◽  
pp. 121-150 ◽  
Author(s):  
IMED BACHAR ◽  
HABIB MÂAGLI ◽  
NOUREDDINE ZEDDINI
Keyword(s):  
Green Function ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Closed Ball ◽  
Dirichlet Boundary Conditions ◽  
Kato Class ◽  
Nonlinear Elliptic ◽  
Existence Of Positive Solutions ◽  
The Green Function ◽  
Class Of Functions

Let [Formula: see text] be the Green function of (-Δ)m, m ≥ 1, on the complementary D of the unit closed ball in ℝn, n ≥ 2, with Dirichlet boundary conditions [Formula: see text], 0 ≤ j ≤ m - 1. We establish some estimates on [Formula: see text] including the 3G-Inequality given by (1.3). Next, we introduce a polyharmonic Kato class of functions [Formula: see text] and we exploit the properties of this class to study the existence of positive solutions of some polyharmonic nonlinear elliptic problems.

scholarly journals Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Imed Bachar ◽  
Habib Mâagli ◽  
Said Mesloub
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Nonlinear Problem ◽  
Existence And Uniqueness ◽  
Blow Up ◽  
Continuous Solution ◽  
Global Estimates ◽  
Nonnegative Continuous Function

The aim of this paper is to establish existence and uniqueness of a positive continuous solution to the following singular nonlinear problem. {-t1-ntn-1u′′=a(t)uσ,  t∈(0,1),  limt→0⁡tn-1u′(t)=0,  u(1)=0}, where n≥3,σ<1, and a denotes a nonnegative continuous function that might have the property of being singular at t=0 and /or t=1 and which satisfies certain condition associated to Karamata class. We emphasize that the nonlinearity might also be singular at u=0, while the solution could blow-up at 0. Our method is based on the global estimates of potential functions and the Schauder fixed point theorem.

scholarly journals Existence of Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Caixia Guo ◽  
Jianmin Guo ◽  
Ying Gao ◽  
Shugui Kang
Keyword(s):  
Green Function ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Fractional Differential ◽  
The Green Function

This paper is concerned with the two-point boundary value problems of nonlinear finite discrete fractional differential equations. On one hand, we discuss some new properties of the Green function. On the other hand, by using the main properties of Green function and the Krasnoselskii fixed point theorem on cones, some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established.

scholarly journals Construction on the Green function for Vallee-Poussin problem for nonlinear system of differential equations

2013 ◽  
Vol 5 (1) ◽  
pp. 121-128
Author(s):  
R.I. Sobkovich ◽  
A.I. Kazmerchuk
Keyword(s):  
Green Function ◽  
Nonlinear System ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Uniqueness Theorems ◽  
System Of Differential Equations ◽  
Existence And Uniqueness Theorems ◽  
Iterative Schemes ◽  
The Green Function

Existence and uniqueness theorems of solution of n-point Vallee-Poussin problem for system of nonlinear differential equations are proved. Iterative schemes for finding them are proposed.

Sign in / Sign up

Export Citation Format

Share Document