Existence results for a class of degenerate quasilinear elliptic systems

2011 ◽  
Vol 51 (4) ◽  
pp. 451-460
Author(s):  
Ghasem A. Afrouzi ◽  
Somayeh Mahdavi
Keyword(s):  
Elliptic Systems ◽  
Existence Results ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

Boundedness and blow-up of solutions for a nonlinear elliptic system

2014 ◽  
Vol 25 (09) ◽  
pp. 1450091 ◽  
Author(s):  
Dragos-Patru Covei
Keyword(s):  
Stochastic Processes ◽  
Elliptic System ◽  
Blow Up ◽  
Elliptic Systems ◽  
Existence Results ◽  
Nonlinear Elliptic System ◽  
Unbounded Solutions ◽  
Nonlinear Elliptic ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

The main objective in this paper is to obtain the existence results for bounded and unbounded solutions of some quasilinear elliptic systems. Related results as obtained here have been established recently in [C. O. Alves and A. R. F. de Holanda, Existence of blow-up solutions for a class of elliptic systems, Differ. Integral Eqs.26(1/2) (2013) 105–118]. Also, we present some references to give the connection between these types of problems with probability and stochastic processes, hoping that these are interesting for the audience of analysts likely to read this paper.

scholarly journals Existence results for a class of (p,q) Laplacian systems

2010 ◽  
Vol 15 (4) ◽  
pp. 397-403
Author(s):  
G. A. Afrouzi ◽  
M. Mirzapour
Keyword(s):  
Nontrivial Solution ◽  
Elliptic Systems ◽  
Existence Results ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

We establish the existence of a nontrivial solution for inhomogeneous quasilinear elliptic systems:−∆pu = λ a(x) u |u|γ−2 + α (α + β)–1 b(x) u |u|α−2 |v|β + f    in Ω,−∆qv = µ d(x) v |v|γ−2 + β (α + β)–1 b(x) |u|α v |v|β−2 + g    in Ω,(u,v) ∈ W01,p(Ω) × W01,q(Ω).Our result depending on the local minimization.

scholarly journals Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the ()-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Armin Hadjian ◽  
Saleh Shakeri
Keyword(s):  
Multiple Solutions ◽  
Main Tool ◽  
Elliptic Systems ◽  
Existence Results ◽  
Laplacian Operator ◽  
Quasilinear Elliptic System ◽  
Critical Point Theorem ◽  
Quasilinear Elliptic Systems ◽  
Double Eigenvalue ◽  
Quasilinear Elliptic

Existence results of three weak solutions for a Dirichlet double eigenvalue quasilinear elliptic system involving the ()-Laplacian operator, under suitable assumptions, are established. Our main tool is based on a recent three-critical-point theorem obtained by Ricceri. We also give some examples to illustrate the obtained results.

On strongly quasilinear elliptic systems with weak monotonicity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Elhoussine Azroul ◽  
Farah Balaadich
Keyword(s):  
Elliptic System ◽  
Sobolev Spaces ◽  
Elliptic Systems ◽  
Existence Results ◽  
Young Measures ◽  
Quasilinear Elliptic System ◽  
Quasilinear Elliptic Systems ◽  
Weak Monotonicity ◽  
Quasilinear Elliptic

Abstract In this paper, we prove existence results in the setting of Sobolev spaces for a strongly quasilinear elliptic system by means of Young measures and mild monotonicity assumptions.

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.

Sign in / Sign up

Export Citation Format

Share Document