标题： 半线性椭圆边值问题在任意开集上的解的存在性 显示英文标题

标题： Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets

摘要： 我们证明了在任意开集上半线性椭圆Dirichlet问题弱解的存在性。 我们不对开集做任何假设，对半线性性仅做非常温和的正则性假设，并加上一个依赖于最优Poincare-Steklov常数的强制性假设。 证明基于将Schaefer不动点定理应用于一系列截断问题。 我们陈述了一个简单的唯一性结果。 我们还将这些结果推广到Robin边界条件。 显示英文摘要

摘要： We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set. We make no assumptions about the open set, very mild regularity assumptions on the semilinearity, plus a coerciveness assumption which depends on the optimal Poincare-Steklov constant. The proof is based on Schaefer's fixed point theorem applied to a sequence of truncated problems. We state a simple uniqueness result. We also generalize the results to Robin boundary conditions.