Semilinear elliptic equations and fixed points
Copyright policy )Semilinear elliptic equations and fixed points
In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $��\subset\mathbb{R}^N$, $N\geq 3$, 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.
4 pages
Krasnoselskii fixed point theorem, Fixed-point theorems, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, 35J25, 47H10, semilinear elliptic equations, FOS: Mathematics, fixed point theorem, Analysis of PDEs (math.AP)
Krasnoselskii fixed point theorem, Fixed-point theorems, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, 35J25, 47H10, semilinear elliptic equations, FOS: Mathematics, fixed point theorem, Analysis of PDEs (math.AP)
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