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    Bifurcation for some quasilinear operators

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    URI: http://hdl.handle.net/10835/581
    ISSN: 0308-2105
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    Author/s
    Arcoya, David; Carmona Tapia, José; Pellacci, Benedetta
    Date
    2001
    Abstract
    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.
    Palabra/s clave
    Mathematics
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    • Artículos de revista Dpto. Matemáticas [119]

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