Semilinear elliptic equations with uniform blow-up on the boundary. (English) Zbl 0802.35042

Summary: We prove the existence and the uniqueness of a solution \(u\) of \(-Lu + h | u |^{\alpha - 1} u = f\) in some open domain \(G \subset\mathbb R^ d\), where \(L\) is a strongly elliptic operator, \(f\) a nonnegative function, and \(\alpha>1\), under the assumption that \(\partial G\) is a \(C^ 2\) compact hypersurface, \(\lim_{x \to \partial G} (\text{dist} (x, \partial G))^{2 \alpha/(\alpha - 1)} f(x) = 0\), and \(\lim_{x \to \partial G} u(x) = \infty\).


35J61 Semilinear elliptic equations
35B44 Blow-up in context of PDEs
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