Existence theorems for a semilinear elliptic boundary value problem

Salvatore Marano

ArticleOriginal scientific text

Title

Existence theorems for a semilinear elliptic boundary value problem

Authors ¹

Affiliations

Dipartimento di Matematica Università di Catania Viale A. Doria 6 95125 Catania, Italy

Abstract

Let Ω be a bounded domain in

ℝ^{n}

, n ≥ 3, with a smooth boundary ∂Ω; let L be a linear, second order, elliptic operator; let f and g be two real-valued functions defined on Ω × ℝ such that f(x,z) ≤ g(x,z) for almost every x ∈ Ω and every z ∈ ℝ. In this paper we prove that, under suitable assumptions, the problem { f(x,u) ≤ Lu ≤ g(x,u) in Ω, u = 0 on ∂Ω, has at least one strong solution !$!u ∈ W^{2,p}(Ω) ∩ W^{1,p}_0(Ω). Next, we present some remarkable special cases.

Keywords

ENG

elliptic differential inclusions, semilinear elliptic equations, strong solutions

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Title

Existence theorems for a semilinear elliptic boundary value problem

Affiliations

Abstract

Keywords

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