Semilinear elliptic equations and fixed points

Barroso, Cleon

doi:10.1090/S0002-9939-04-07718-4

Semilinear elliptic equations and fixed points
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by Cleon S. Barroso PDF

Proc. Amer. Math. Soc. 133 (2005), 745-749 Request permission

Abstract:

In this paper, we deal with a class of semilinear elliptic equations in a bounded domain $\Omega \subset \mathbb {R}^N$, $N\geq 3$, with $C^{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.

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