Nonnegative Solutions for Weakly Nonlinear Elliptic Equations

Allegretto, Walter

Canadian journal of mathematics, Tome 36 (1984) no. 1, pp. 71-83

Résumé

Let x = (x1, ... xn ) denote a point of Euclidean n space En and set Di = ∂/∂xi for i = 1, ... n. Let Ω denote an exterior domain in En with smooth boundary and consider in Ω the formal elliptic problem: 1 We first consider the problem of finding nonnegative generalized solutions of (1) when τ ≧ 0, τ ≢ 0, and r(x) ≡ 0. Under more stringent conditions on the coefficients and for suitable r(x), we then show the existence of a locally bounded solution. Next, we show that, under stronger assumptions, our main criterion is also necessary. The final arguments are devoted to the consideration of illustrative examples.

Détail

DOI : 10.4153/CJM-1984-006-4

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