Multiplicity of Positive Solutions for Critical Singular Elliptic Systems With Concave-Convex Nonlinearities

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Tsing-San Hsu
Keyword(s):  
Variational Methods ◽  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Systems ◽  
Critical Growth ◽  
Bounded Domains ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this paper, we consider a singular elliptic system with both concave-convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.

Multiple positive solutions for a critical elliptic system with concave—convex nonlinearities

2009 ◽  
Vol 139 (6) ◽  
pp. 1163-1177 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Variational Methods ◽  
Elliptic System ◽  
Positive Solutions ◽  
Critical Growth ◽  
Bounded Domains ◽  
Multiple Positive Solutions ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System

We consider a semilinear elliptic system with both concave—convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.

scholarly journals EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC SYSTEMS INVOLVING CRITICAL HARDY–SOBOLEV EXPONENTS AND SIGN-CHANGING WEIGHT FUNCTION

2012 ◽  
Vol 17 (3) ◽  
pp. 330-350 ◽  
Author(s):  
Nemat Nyamoradi
Keyword(s):  
Weight Function ◽  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Systems ◽  
Multiple Positive Solutions ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Systems ◽  
Sobolev Exponent ◽  
Quasilinear Elliptic

In this paper, we consider a class of quasilinear elliptic systems with weights and the nonlinearity involving the critical Hardy–Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.

scholarly journals On Dirichlet problem for fractional p-Laplacian with singular non-linearity

2016 ◽  
Vol 8 (1) ◽  
pp. 52-72 ◽  
Author(s):  
Tuhina Mukherjee ◽  
Konijeti Sreenadh
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Smooth Boundary ◽  
Critical Growth ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

Abstract In this article, we study the following fractional p-Laplacian equation with critical growth and singular non-linearity: (-\Delta_{p})^{s}u=\lambda u^{-q}+u^{\alpha},\quad u>0\quad\text{in }\Omega,% \qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega, where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega} , {n>sp} , {s\in(0,1)} , {\lambda>0} , {0<q\leq 1} and {1<p<\alpha+1\leq p^{*}_{s}} . We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ.

scholarly journals Existence, Nonexistence and Multiplicity Results for Positive Radial Solutions of n−dimensional Elliptic System

2021 ◽  
pp. 35-45
Author(s):  
Yalin Shen
Keyword(s):  
Elliptic System ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Information Science ◽  
Elliptic Systems ◽  
Point Index ◽  
Radial Solutions ◽  
Multiplicity Results ◽  
Positive Radial Solutions ◽  
Multiplicity Of Positive Solutions

Aims/ Objectives: In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the n−dimensional elliptic system  systems have been widely studied, but there is relatively little research on n-dimensional elliptic systems. We are very interested in this subject and want to study it. We give new conclusions on the existence, nonexistence and multiplicity of positive solutions for the n-dimensional elliptic system. Study Design: Study on the existence, nonexistence and multiplicity of positive solutions. Place and Duration of Study: School of Applied Science, Beijing Information Science & Technology University, September 2019 to present. Methodology: We prove the existence, nonexistence and multiplicity of positive solutions by the results of fixed point index. Results: We give new conclusions of existence, nonexistence and multiplicity of positive solutionsfor the system. Conclusion: We prove the existence, nonexistence and multiplicity of positive solutions to the n-dimensional elliptic system   and give new conclusions.

Positive solutions of fractional elliptic equation with critical and singular nonlinearity

2017 ◽  
Vol 6 (3) ◽  
pp. 327-354 ◽  
Author(s):  
Jacques Giacomoni ◽  
Tuhina Mukherjee ◽  
Konijeti Sreenadh
Keyword(s):  
Elliptic Equation ◽  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Smooth Boundary ◽  
Critical Growth ◽  
Content Type ◽  
Singular Nonlinearity ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

AbstractIn this article, we study the following fractional elliptic equation with critical growth and singular nonlinearity:(-\Delta)^{s}u=u^{-q}+\lambda u^{{2^{*}_{s}}-1},\qquad u>0\quad\text{in }% \Omega,\qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega,where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega}, {n>2s}, {s\in(0,1)}, {\lambda>0}, {q>0} and {2^{*}_{s}=\frac{2n}{n-2s}}. We use variational methods to show the existence and multiplicity of positive solutions with respect to the parameter λ.

Multiplicity of positive solutions for a class of problems with critical growth in ℝN

2009 ◽  
Vol 52 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Claudianor O. Alves ◽  
Daniel C. de Morais Filho ◽  
Marco A. S. Souto
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Continuous Functions ◽  
Critical Growth ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

AbstractUsing variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems:where λ,β∈(0,∞), q∈(1,2*−1), 2*=2N/(N−2), N≥3, V,Z:ℝN→ℝ are continuous functions verifying some hypotheses.

scholarly journals Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yong-Yi Lan ◽  
Xian Hu ◽  
Bi-Yun Tang
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents. Using variational methods, we establish the existence and multiplicity of positive solutions for the problem.

Existence and multiplicity of positive solutions for a critical weight elliptic system in ℝN

2020 ◽  
pp. 2050027
Author(s):  
João Pablo Pinheiro da Silva ◽  
Claudionei Pereira de Oliveira
Keyword(s):  
Elliptic System ◽  
Positive Solutions ◽  
Homogeneous Function ◽  
Critical Weight ◽  
Partial Derivatives ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
Derivatives Of

In this work, we study the following problem [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are the partial derivatives of the homogeneous function [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

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