摘要
In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.
In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.
基金
supported by the Natural Science Foundation of Henan Province(15A110050)
