Treffer: Positive solutions for the p-Laplacian with dependence on the gradient

Title:
Positive solutions for the p-Laplacian with dependence on the gradient
Authors:
BUENO, H, ERCOLE, G, ZUMPANO, A, FERREIRA, W. M
Source:
Nonlinearity (Bristol. Print). 25(4):1211-1234
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 31 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Equations algébriques et transcendantes non linéaires, Nonlinear algebraic and transcendental equations, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Comportement asymptotique, Asymptotic behavior, Comportamiento asintótico, Condition aux limites, Boundary condition, Condiciones límites, Contraste, Contrast, Croissance, Growth, Crecimiento, Existence solution, Existence of solution, Existencia de solución, Fonction poids, Weight function, Función peso, Laplacien p, P laplacian, Laplaciana p, Non linéarité, Nonlinearity, No linealidad, Physique mathématique, Mathematical physics, Física matemática, Résolution problème, Problem solving, Resolución problema, Solution positive, Positive solution, Solución positiva, Théorème point fixe, Fixed point theorem, Teorema punto fijo, Valeur propre, Eigenvalue, Valor propio, 58J20, 65F15, 65H17, Condition Dirichlet, Domaine borné, Théorème Schauder
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Depto. de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, 30.123-970, Brazil
Depto. de Matemática, Universidade Federal de Ouro Preto, Ouro Preto, 35.400-000, Brazil
ISSN:
0951-7715
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=25768314
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
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.25768314
Database:
PASCAL Archive

Weitere Informationen

We prove a result of existence of positive solutions for the p-Laplacian problem ―Δpu = ω(x)f(u, |∇u|) with Dirichlet boundary condition in a bounded domain Ω C ℝN, where ω is a weight function. As in previous results by the authors, and in contrast with the hypotheses usually made, no asymptotic behaviour is assumed on f, but simple geometric assumptions in a neighbourhood of the first eigenvalue of the p-Laplacian operator. We start by solving the problem in a radial domain by applying the Schauder fixed point theorem and this result is used to construct an ordered pair of sub- and super-solution, also valid for nonlinearities which are super-linear at both the origin and +∞, which is a remarkable fact. We apply our method to the p-growth problem ―Δpu = λu(x)q―1(1 + |∇u(x)|p) (1 < q < p) in Ω with Dirichlet boundary conditions and give examples of super-linear nonlinearities which are also handled by our method.