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

Salvatore A. Marano

doi:10.4171/zaa/969

JournalszaaVol. 19, No. 2pp. 575–582

Existence Results for the Equation $-Δ u = f (x, u) in R^{n}$

Salvatore A. Marano
Università degli Studi di Catania, Italy

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

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Abstract

Strong solutions to the class of semilinear elliptic equations $-Δ u = f (x, u) o n t h ee n t i res p a ce an d w i t h p oss ib l ys u p ercr i t i c a l g ro wt h f or$ f(x, \cdot)$ are obtained by mainly using fixed points arguments. The case of discontinuous non-linearities is then examined.

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Salvatore A. Marano, Existence Results for the Equation $-Δ u = f (x, u) in R^{n}$ . Z. Anal. Anwend. 19 (2000), no. 2, pp. 575–582

DOI 10.4171/ZAA/969