scholarly journals Combined Effects in Singular Elliptic Problems in Punctured Domain

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Imed Bachar ◽  
Habib Mâagli ◽  
Hassan Eltayeb
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Blow Up ◽  
Continuous Solution ◽  
Combined Effects ◽  
Regularly Varying Functions ◽  
Nonlinear Elliptic ◽  
Elliptic Differential Equations ◽  
Global Estimates ◽  
Punctured Domain

The paper deals with nonlinear elliptic differential equations subject to some boundary value conditions in a regular bounded punctured domain. By means of properties of slowly regularly varying functions at zero and the Schauder fixed-point theorem, we establish the existence of a positive continuous solution for the suggested problem. Global estimates on such solution, which could blow up at the origin, are also obtained.

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 Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Imed Bachar ◽  
Said Mesloub
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Blow Up ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Fractional Boundary Value Problems

We consider singular nonlinear Hadamard fractional boundary value problems. Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. Finally, some examples are provided to explain the applications of the results.

scholarly journals On a singular sublinear polyharmonic problem

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Sonia Ben Othman
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Unit Ball ◽  
Existence Result ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Combined Effects ◽  
Polyharmonic Equations

This paper deals with a class of singular nonlinear polyharmonic equations on the unit ballBinℝn (n≥2)where the combined effects of a singular and a sublinear term allow us by using the Schauder fixed point theorem to establish an existence result for the following problem:(−Δ)mu=φ(⋅,u)+ψ(⋅,u)inB(in the sense of distributions),u>0,lim⁡|x|→1u(x)/(1−|x|)m−1=0. Our approach is based on estimates for the polyharmonic Green function onBwith zero Dirichlet boundary conditions.

scholarly journals Existence and asymptotic properties of singular solutions of nonlinear elliptic equations in $R^{n}\backslash\{0\}$

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Imed Bachar ◽  
Entesar Aljarallah
Keyword(s):  
Elliptic Equations ◽  
Blow Up ◽  
Continuous Solution ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Nonlinear Elliptic Equations ◽  
Weighted Function ◽  
Distributional Sense ◽  
Nonlinear Elliptic ◽  
Semilinear Problem

AbstractWe consider the following singular semilinear problem $$ \textstyle\begin{cases} \Delta u(x)+p(x)u^{\gamma }=0,\quad x\in D ~(\text{in the distributional sense}), \\ u>0,\quad \text{in }D, \\ \lim_{ \vert x \vert \rightarrow 0} \vert x \vert ^{n-2}u(x)=0, \\ \lim_{ \vert x \vert \rightarrow \infty }u(x)=0,\end{cases} $$ { Δ u ( x ) + p ( x ) u γ = 0 , x ∈ D ( in the distributional sense ) , u > 0 , in  D , lim | x | → 0 | x | n − 2 u ( x ) = 0 , lim | x | → ∞ u ( x ) = 0 , where $\gamma <1$ γ < 1 , $D=\mathbb{R}^{n}\backslash \{0\}$ D = R n ∖ { 0 } ($n\geq 3$ n ≥ 3 ) and p is a positive continuous function in D, which may be singular at $x=0$ x = 0 . Under sufficient conditions for the weighted function $p(x)$ p ( x ) , we prove the existence of a positive continuous solution on D, which could blow-up at the origin. The global asymptotic behavior of this solution is also obtained.

scholarly journals Singular nonlinear elliptic equations inRn

1998 ◽  
Vol 3 (3-4) ◽  
pp. 411-423 ◽  
Author(s):  
C. O. Alves ◽  
J. V. Goncalves ◽  
L. A. Maia
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Equations ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Continuous Functions ◽  
Generalized Solutions ◽  
Radial Functions ◽  
Nonlinear Elliptic ◽  
Singular Nonlinear Equations

This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the form−Δu+a(x)u=h(x)u−γinRnwherea,hare given, not necessarily continuous functions, andγis a positive number. We explore both situations wherea,hare radial functions, withabeing eventually identically zero, and cases where no symmetry is required from eitheraorh. Schauder's fixed point theorem, combined with penalty arguments, is exploited.

scholarly journals Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Imed Bachar ◽  
Habib Mâagli ◽  
Hassan Eltayeb
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Continuous Solution ◽  
Boundary Value ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

This paper deals with the following boundary value problem D α u t = f t , u t , t ∈ 0 , 1 , u 0 = u 1 = D α − 3 u 0 = u ′ 1 = 0 , where 3 < α ≤ 4 , D α is the Riemann-Liouville fractional derivative, and the nonlinearity f , which could be singular at both t = 0 and t = 1 , is required to be continuous on 0 , 1 × ℝ satisfying a mild Lipschitz assumption. Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a unique continuous solution u satisfying u t ≤ c ω t , for   t ∈ 0 , 1   and   c > 0 , where ω t ≔ t α − 2 1 − t 2 .

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
Sign in / Sign up

Export Citation Format

Share Document