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  • Explosive solutions of elliptic equations with absorption and non-linear gradient term
    Ghergu, Marius ; Niculescu, Constantin P. ; Rǎdulescu, Vicenţiu, 1958-
    Let ▫$f$▫ be a non-decreasing ▫$C^1$▫-function such that ▫$f>0$▫ on ▫$(0,\infty)$▫, ▫$f(0)=0$▫, ▫$\int^\infty_11/ \sqrt{F(t)}dt < \infty$▫ and ▫$F(t)/f^{2/a} (t)\to 0$▫ as ▫$t\to\infty$▫, where ... ▫$F(t) = \int^t_0 f(s)ds$▫ and ▫$a \in (0,2]$▫. We prove the existence of positive large solutions to the equation ▫$\Delta u + q(x) |\nabla u|^a = p(x)f(u)$▫ in a smooth bounded domain ▫$\Omega \subset\Bbb R^N$▫, provided that ▫$p,q$▫ are non-negative continuous functions so that any zero of ▫$p$▫ is surrounded by a surface strictly included in ▫$\Omega$▫ on which ▫$p$▫ is positive. Under additional hypotheses on ▫$p$▫ we deduce the existence of solutions if ▫$\Omega$▫ is unbounded.
    Source: Proceedings of the Indian Academy of Sciences. Mathematical sciences. - ISSN 0253-4142 (Vol. 112, no. 3, 2002, str. 441-451)
    Type of material - article, component part
    Publish date - 2002
    Language - english
    COBISS.SI-ID - 15269721

    Link(s):

    http://dx.doi.org/10.1007/BF02829796

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