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  • On a class of sublinear singular elliptic problems with convection term
    Ghergu, Marius ; Rǎdulescu, Vicenţiu, 1958-
    We establish several results related to the existence, nonexistence and bifurcation of positive solutions for the boundary value problem ▫$$-\Delta u + K(x)g(u) + |\nabla u|^a = \lambda f(x,u) \quad ... \text{in} \Omega,$$▫ ▫$$u = 0\quad \text{ on} \partial\Omega,$$▫ where ▫$\Omega \subset {\Bbb R}^N (N \geq 2)$▫ is a smooth bounded domain, ▫$0 <a \leq 2▫, ▫\lambda$▫ is a positive parameter, and ▫$f$▫ is smooth and has sublinear growth in its second argument. The main feature of this paper consists in the presence of the singular nonlinearity ▫$g$▫ combined with the convection term ▫$|\nabla u|^a$▫. Our approach takes into account both the sign of the potential ▫$K$▫ and the decay rate around the origin of the singular nonlinearity ▫$g$▫. The proofs are based on various techniques related to the maximum principle for elliptic equations.
    Source: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 311, no. 2, 2005, str. 635-646)
    Type of material - article, component part
    Publish date - 2005
    Language - english
    COBISS.SI-ID - 15064665

    Link(s):

    http://dx.doi.org/10.1016/j.jmaa.2005.03.012

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