# The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations

@inproceedings{Hirata2006TheBG, title={The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations}, author={Kentaro Hirata}, year={2006} }

- Published 2006
DOI:10.1007/s00208-007-0163-6

We investigate the boundary growth of positive superharmonic functions u on a bounded domain Ω in R, n ≥ 3, satisfying the nonlinear elliptic inequality 0 ≤ −∆u ≤ cδΩ(x)u in Ω, where c > 0, α ≥ 0 and p > 0 are constants, and δΩ(x) is the distance from x to the boundary of Ω. The result is applied to show a Harnack inequality for such superharmonic functions. Also, we study the existence of positive solutions, with singularity on the boundary, of the nonlinear elliptic equation −∆u + V u = f(x… CONTINUE READING