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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 2, 2000, pp. 575–582
DOI: 10.4171/ZAA/969

Published online: 2000-06-30

Existence Results for the Equation $– \Delta u = f(x, u) in \mathbb R^n$

Salvatore A. Marano[1]

(1) Università degli Studi di Catania, Italy

Strong solutions to the class of semilinear elliptic equations $– \Delta u = f(x, u) on the entire space and with possibly supercritical growth for $f(x, \cdot)$ are obtained by mainly using fixed points arguments. The case of discontinuous non-linearities is then examined.

Keywords: Elliptic equations in the whole space, discontinuous non-linearities, strong solutions

Marano Salvatore: Existence Results for the Equation $– \Delta u = f(x, u) in \mathbb R^n$. Z. Anal. Anwend. 19 (2000), 575-582. doi: 10.4171/ZAA/969