scholarly journals EXISTENCE OF SOLUTIONS FOR A DEGENERATE QUASILINEAR ELLIPTIC SYSTEM IN BOUNDED DOMAIN

2013 ◽  
Vol 3 (1) ◽  
pp. 1-9
Author(s):  
G. A. Afrouzi ◽  
◽  
N. T. Chung ◽  
M. Mirzapour ◽  
Keyword(s):  
Elliptic System ◽  
Bounded Domain ◽  
Existence Of Solutions ◽  
Quasilinear Elliptic System ◽  
Quasilinear Elliptic

scholarly journals Quasilinear Riccati-Type Equations with Oscillatory and Singular Data

2020 ◽  
Vol 20 (2) ◽  
pp. 373-384
Author(s):  
Quoc-Hung Nguyen ◽  
Nguyen Cong Phuc
Keyword(s):  
Elliptic Operator ◽  
Bounded Domain ◽  
Existence Of Solutions ◽  
Type Equation ◽  
Linear Range ◽  
Measure Data ◽  
Regularity Conditions ◽  
Compactly Supported ◽  
Singular Data ◽  
Quasilinear Elliptic

AbstractWe characterize the existence of solutions to the quasilinear Riccati-type equation\left\{\begin{aligned} \displaystyle-\operatorname{div}\mathcal{A}(x,\nabla u)% &\displaystyle=|\nabla u|^{q}+\sigma&&\displaystyle\phantom{}\text{in }\Omega,% \\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{on }\partial% \Omega,\end{aligned}\right.with a distributional or measure datum σ. Here {\operatorname{div}\mathcal{A}(x,\nabla u)} is a quasilinear elliptic operator modeled after the p-Laplacian ({p>1}), and Ω is a bounded domain whose boundary is sufficiently flat (in the sense of Reifenberg). For distributional data, we assume that {p>1} and {q>p}. For measure data, we assume that they are compactly supported in Ω, {p>\frac{3n-2}{2n-1}}, and q is in the sub-linear range {p-1<q<1}. We also assume more regularity conditions on {\mathcal{A}} and on {\partial\Omega\Omega} in this case.

MULTIPLICITY RESULTS FOR A QUASILINEAR ELLIPTIC SYSTEM VIA MORSE THEORY

2005 ◽  
Vol 07 (02) ◽  
pp. 227-249 ◽  
Author(s):  
SILVIA CINGOLANI ◽  
MONICA LAZZO ◽  
GIUSEPPINA VANNELLA
Keyword(s):  
Banach Space ◽  
Elliptic System ◽  
Laplace Operator ◽  
Morse Theory ◽  
Quasilinear Elliptic System ◽  
Quasilinear Equations ◽  
Multiplicity Results ◽  
New Perturbation ◽  
Quasilinear Elliptic

In this work we prove some multiplicity results for solutions of a system of elliptic quasilinear equations, involving the p-Laplace operator (p > 2). The proof are based on variational and topological arguments and makes use of new perturbation results in Morse theory for the Banach space [Formula: see text].

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