scholarly journals Existence of positive solutions for quasilinear elliptic systems with Sobolev critical exponents

2011 ◽  
pp. 57-71
Author(s):  
Xiaoyan Cao ◽  
Zuodong Yang
Keyword(s):  
Positive Solutions ◽  
Critical Exponents ◽  
Elliptic Systems ◽  
Quasilinear Elliptic Systems ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic

scholarly journals Quasilinear elliptic systems in divergence form associated to general nonlinearities

2018 ◽  
Vol 7 (4) ◽  
pp. 425-447 ◽  
Author(s):  
Lorenzo D’Ambrosio ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Systems Of Equations ◽  
Quasilinear Elliptic Systems ◽  
Open Set ◽  
Priori Estimates ◽  
Quasilinear Elliptic

AbstractThe paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case {\Omega=\mathbb{R}^{N}}, we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.

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 Monotonicity and symmetry of positive solutions to degenerate quasilinear elliptic systems in half-spaces and strips

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Phuong Le ◽  
Hoang-Hung Vo
Keyword(s):  
Positive Solutions ◽  
Elliptic Systems ◽  
Method Of Moving Planes ◽  
Quasilinear Elliptic Systems ◽  
Moving Planes ◽  
Quasilinear Elliptic

<p style='text-indent:20px;'>By means of the method of moving planes, we study the monotonicity of positive solutions to degenerate quasilinear elliptic systems in half-spaces. We also prove the symmetry of positive solutions to the systems in strips by using similar arguments. Our work extends the main results obtained in [<xref ref-type="bibr" rid="b16">16</xref>,<xref ref-type="bibr" rid="b20">20</xref>] to the system, in which substantial differences with the single cases are presented.</p>

scholarly journals Quasilinear Elliptic Equations with Hardy-Sobolev Critical Exponents: Existence and Multiplicity of Nontrivial Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guanwei Chen
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Critical Exponents ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic

We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.

scholarly journals Singular Quasilinear Elliptic Systems with (super-) Homogeneous Condition

2020 ◽  
pp. 151-159
Author(s):  
Hana Didi ◽  
Brahim Khodja ◽  
Abdelkrim Moussaoui
Keyword(s):  
Positive Solutions ◽  
Elliptic Systems ◽  
Homogeneous Condition ◽  
Singular Terms ◽  
Singular Equations ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic ◽  
Perturbation Arguments

In this paper we establish existence, nonexistence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (super-) homogeneous condition. The approach is based on sub-supersolution methods for systems of quasilinear singular equations combined with perturbation arguments involving singular terms

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