具有低阶项的非局部椭圆及抛物问题的正解(英文)

Positive Solutions of Elliptic and Parabolic Problems With Nonlocal Lower Order Terms

考虑了非局部边值问题{-a(∫Ω|u|qdx)Δu+b(l(u))u=f(x,u), in Ω,u=0, on Ω,及其相应的非局部抛物问题的正解存在性.其中Ω是RN中的有界光滑区域,a和b是给定的函数.利用Galerkin方法,首先获得了具有低阶项的非局部椭圆问题正解的存在性,进一步证明了抛物问题正解的存在性.

The existence of positive solution about nonlocal boundary problems with lower order nonlocal terms {-a（∫Ω｜u｜^qdx）Δu＋b（l（u））u=f（x,u）, in Ω, u=0, on δΩ, and its parabolic counterpart were considered where Ω was a bounded smooth domain of R^N（N 〉 2） , a and b were given function. By using Galerkin method, the existence of positive solution for the nonlocal elliptic problems was obtained, moreover, the existence of positive solution for the evolution case was proved.