Infinitely many singular radial solutions for quasilinear elliptic systems

2015 ◽  
Vol 08 (03) ◽  
pp. 1550045
Author(s):  
Khalid Iskafi ◽  
Abdelaziz Ahammou
Keyword(s):  
Elliptic Systems ◽  
Sufficient Condition ◽  
Quasilinear Elliptic System ◽  
Radial Solutions ◽  
Quasilinear Elliptic Systems ◽  
Monotone Iterations ◽  
Variational Structure ◽  
Structure Formula ◽  
Quasilinear Elliptic ◽  
Schauder Theorem

We prove the existence of infinitely many singular radial positive solutions for a quasilinear elliptic system with no variational structure [Formula: see text] where [Formula: see text] is the unit ball of [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text] are non-negative functions. We separate two fundamental classes (the sublinear and superlinear class), and we use respectively the Leray–Schauder Theorem and a method of monotone iterations to obtain the existence of many solutions with a property of singularity around the origin. Finally, we give a sufficient condition for the non-existence.

On the Existence of Boundary Blow-up Solutions for a General Class of Quasilinear Elliptic Systems

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Sonia Ben Othman ◽  
Rym Chemmam ◽  
Paul Sauvy
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
General Class ◽  
Blow Up ◽  
Elliptic Systems ◽  
Quasilinear Elliptic System ◽  
Smooth Bounded Domain ◽  
Quasilinear Elliptic Systems ◽  
System P ◽  
Quasilinear Elliptic

AbstractIn this paper, we investigate the following quasilinear elliptic system (P) with explosive boundary conditions:ΔΔwhere Ω is a smooth bounded domain of ℝ

scholarly journals Positive radial solutions for some quasilinear elliptic systems in exterior domains

2006 ◽  
Vol 5 (3) ◽  
pp. 571-581 ◽  
Author(s):  
João Marcos do Ó ◽  
◽  
Sebastián Lorca ◽  
Justino Sánchez ◽  
Pedro Ubilla ◽  
...  
Keyword(s):  
Elliptic Systems ◽  
Radial Solutions ◽  
Exterior Domains ◽  
Quasilinear Elliptic Systems ◽  
Positive Radial Solutions ◽  
Quasilinear Elliptic

scholarly journals Large Solutions of Quasilinear Elliptic System of Competitive Type: Existence and Asymptotic Behavior

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Lin Wei ◽  
Zuodong Yang
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic System ◽  
Smooth Boundary ◽  
Upper And Lower Solutions ◽  
Elliptic Systems ◽  
Quasilinear Elliptic System ◽  
Localization Method ◽  
Large Solutions ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

We study the existence and asymptotic behavior of positive solutions for a class of quasilinear elliptic systems in a smooth boundary via the upper and lower solutions and the localization method. The main results of the present paper are new and extend some previous results in the literature.

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 of resonant type and nonlinear eigenvalue problems

2002 ◽  
Vol 7 (3) ◽  
pp. 155-167 ◽  
Author(s):  
Pablo L. de Nàpoli ◽  
M. Cristina Mariani
Keyword(s):  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problem ◽  
Minimax Theorem ◽  
Elliptic Systems ◽  
Infinitely Many Solutions ◽  
Quasilinear Elliptic System ◽  
Nonlinear Eigenvalue Problems ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic ◽  
Nonlinear Eigenvalue

This work is devoted to the study of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many solutions of a related nonlinear eigenvalue problem. Applying an abstract minimax theorem, we obtain a solution of the quasilinear system−Δpu=Fu(x, u, v), −Δqv=F v(x, u, v), under conditions involving the first and the second eigenvalues.

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