Semilinear Elliptic Equations and Fixed Points

Details Semilinear Elliptic Equations and Fixed Points Semilinear Elliptic Equations and Fixed Points

2003-10-30

arxiv.org/abs/math/0310477v1

Mathematics

Analysis of PDEs

4 pages

Scientific paper

In this paper, we deal with a class of semilinear elliptic equation in a
bounded domain $\Omega\subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$
boundary. Using a new fixed point result of the Krasnoselskii's 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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