Skip to content Skip to navigation

On the Existence of Positive Solutions of Nonlinear Dirichlet Problems for the Fractional Laplacian in the Half Space

Volume 4, Number 1 (2013), 67 - 92

On the Existence of Positive Solutions of Nonlinear Dirichlet Problems for the Fractional Laplacian in the Half Space

Communicated By: 
Alain Haraux
Price: $20.00

Abstract

We investigate in this paper existence results of positive continuous solutions for some nonlinear boundary value problems based on the fractional Laplacian (−Δ)
α/2 , 0< α <2, in the upper half space Rd+, d ≥2. Our arguments are based on potential theory and properties of an appropriate Kato class of functions K∞α (Rd+).