On the Existence and Shape of Solutions to a Semilinear Neumann Problem
Wei‐Ming Ni, Izumi Takagi · Birkhäuser Boston eBooks · 1992
In this article we shall review some recent progress in the study of the Neumann problem for a semilinear elliptic equation. Let Ω be a bounded domain in R N , N ≥ 2, with smooth boundary ∂Ω and let v denote the unit outer normal to ∂Ω. We consider the Neumann problem in which is the Laplace operator, d is a positive constant and throughout the article we assume that unless it is explicitly stated otherwise. (Most of the results below do generalize to a certain class of functions f including t p , and the reader is referred to the original papers cited.)