Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2000-06-30
Existence Results for the Equation $– \Delta u = f(x, u) in \mathbb R^n$Salvatore A. Marano (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