Result: On G-symmetric solutions of a quasilinear elliptic equation involving critical Hardy―Sobolev exponent
Title:
On G-symmetric solutions of a quasilinear elliptic equation involving critical Hardy―Sobolev exponent
Authors:
Source:
Journal of mathematical analysis and applications. 384(2):578-590
Publisher Information:
Amsterdam: Elsevier, 2011.
Publication Year:
2011
Physical Description:
print, 18 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbres et anneaux commutatifs, Commutative rings and algebras, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Optimisation et calcul variationnel numériques, Numerical methods in optimization and calculus of variations, Analyse mathématique, Mathematical analysis, Análisis matemático, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Equation elliptique, Elliptic equation, Ecuación elíptica, Equation quasi linéaire, Quasi linear equation, Ecuación casi lineal, Laplacien p, P laplacian, Laplaciana p, Multiplicité, Multiplicity, Multiplicidad, Méthode analytique, Analytical method, Método analítico, Méthode variationnelle, Variational methods, Non linéarité, Nonlinearity, No linealidad, 13H15, 35Jxx, 49R50, 65K10, 65Kxx, Domaine borné, Exposant critique Sobolev, Problème elliptique, Solution symétrique, Critical Hardy-Sobolev exponent, G-symmetric solution, Quasilinear elliptic equation
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, Soochow University, Suzhou 215006, Jiangsu, China
School of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
School of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
ISSN:
0022-247X
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.24481143
Database:
PASCAL Archive
Further Information
This paper deals with the class of singular quasilinear elliptic problem ― Δpu = μ|u|p―2u |x|p + k(x)|u|p* (s)―2u |x|s + λf(x,u) in Ω, u = 0 on ∂Ω, where Ω ⊂ ℝN is a smooth bounded domain, and Ω is G-symmetric with respect to a subgroup G of O(ℕ), 0 ∈ Ω, 1 < p < N, Δpu = div(|∇u|p―2∇u) is the p-Laplacian, 0 ≤ μ < μ, μ = (N―p p)p, 0 ≤ s < p, λ ≥ 0, p*(s) = (N―s)p N―p, k(x) is continuous and G-symmetric on Ω, and f: Ω × ℝ ↦ ℝ ↦ ℝ is a continuous nonlinearity of lower order satisfying some conditions. By using the variational methods and analytic techniques, we obtain several existence and multiplicity results of G-symmetric solutions under certain hypotheses on μ, λ and k.