Bifurcation for some quasilinear operators

This paper deals with existence, uniqueness and multiplicity results of positive solutions for the quasilinear elliptic boundary-value problem $$\begin{array}{c} -\mbox{div}\, (A(x,u)\nabla u) = f(\lambda,x, u), \quad \mbox{ in } \Omega , \\u = 0, \quad \mbox{ on } \partial \Omega , \end{array} $$...

Ful tanımlama

Detaylı Bibliyografya
Asıl Yazarlar: Arcoya, David, Carmona Tapia, José, Pellacci, Benedetta
Materyal Türü: info:eu-repo/semantics/article
Dil:English
Baskı/Yayın Bilgisi: Cambridge University Press 2012
Konular:
Online Erişim:http://hdl.handle.net/10835/581
Diğer Bilgiler
Özet:This paper deals with existence, uniqueness and multiplicity results of positive solutions for the quasilinear elliptic boundary-value problem $$\begin{array}{c} -\mbox{div}\, (A(x,u)\nabla u) = f(\lambda,x, u), \quad \mbox{ in } \Omega , \\u = 0, \quad \mbox{ on } \partial \Omega , \end{array} $$ where Ω is a bounded open domain in RN with smooth boundary. Under suitable assumptions on the matrix A(x, s), and depending on the behaviour of the function f near u = 0 and near u = +∞, we can use bifurcation theory in order to give a quite complete analysis on the set of positive solutions. We will generalize in different directions some of the results in the papers by Ambrosetti et al., Ambrosetti and Hess, and Artola and Boccardo.