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Zbl 0802.35042
Veron, Laurent
Semilinear elliptic equations with uniform blow-up on the boundary.
(English)
[J] J. Anal. Math. 59, 231-250 (1992). ISSN 0021-7670; ISSN 1565-8538/e

Summary: We prove the existence and the uniqueness of a solution $u$ of $-Lu + h \vert u \vert\sp{\alpha - 1} u = f$ in some open domain $G \subset \bbfR\sp d$, where $L$ is a strongly elliptic operator, $f$ a nonnegative function, and $\alpha>1$, under the assumption that $\partial G$ is a $C\sp 2$ compact hypersurface, $\lim\sb{x \to \partial G} (\text {dist} (x, \partial G))\sp{2 \alpha/(\alpha - 1)} f(x) = 0$, and $\lim\sb{x \to \partial G} u(x) = \infty$.
MSC 2000:
*35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE)

Keywords: semilinear elliptic equations; uniform blow-up on the boundary

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