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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| α-1 u=f in some open domain G d , where L is a strongly elliptic operator, f a nonnegative function, and α>1, under the assumption that G is a C 2 compact hypersurface, lim xG (dist(x,G)) 2α/(α-1) f(x)=0, and lim xG u(x)=.
35J60Nonlinear elliptic equations
35A05General existence and uniqueness theorems (PDE) (MSC2000)
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