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    Bifurcation for quasilinear elliptic singular BVP

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    acmbif_author_version.pdf (270.7Kb)
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    URI: http://hdl.handle.net/10835/576
    ISSN: 0360-5302
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    Author/s
    Carmona Tapia, José; Arcoya, David; Martínez-Aparicio, Pedro J.
    Date
    2011-01-20
    Abstract
    For a continuous function $g\geq 0$ on $(0,+\infty)$ (which may be singular at zero), we confront a quasilinear elliptic differential operator with natural growth in $\nabla u$, $-\Delta u +g(u)|\nabla u|^{2}$, with a power type nonlinearity, $\lambda u^{p}+ f_{0}(x)$. The range of values of the parameter $\lambda$ for which the associated homogeneous Dirichlet boundary value problem admits positive solutions depends on the behavior of $g$ and on the exponent $p$. Using bifurcations techniques we deduce sufficient conditions for the boundedness or unboundedness of the cited range.
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