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

Авторы

  • Stahn Reinhard Institut fur Analysis, Technische Universit¨at Dresden Germany, 01062, Dresden, Helmholtzstr., 10

Аннотация

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set Ω. We make no assumptions about the open set Ω and very mild regularity assumptions on the semilinearity f, plus a coerciveness assumption which depends on the optimal Poincar´e-Steklov constant λ1. 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. Refs 17.

Ключевые слова:

elliptic, semilinear, locally convex, fixed point, arbitrary domain

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Опубликован

01.11.2015

Как цитировать

Reinhard, S. (2015). Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия, 2(4), 576–588. извлечено от https://math-mech-astr-journal.spbu.ru/article/view/11193

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Раздел

Математика