The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations
نویسنده
چکیده
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, u) in Ω, where V and f are Borel measurable functions conditioned by the generalized Kato class.
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