Existence Results for Superlinear Elliptic Equations with Nonlinear Boundary Value Conditions

作     者：Xiao Hui YU 

作者机构：College of Mathematics and Statistics Shenzhen University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第10期

页      面：1655-1680页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by NSFC(Grant Nos.11771300 and 11726634) 

主　　题：Existence result critical exponent trace inequality nonlinear boundary value (PS) condition 

摘      要：In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition{-△u+u=|u|^r-2u in Ω,■u/■v=|u|^q-2u on ■Ω, where Ω■R^N, N≥3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases:(i) Both q and r are subcritical;(ii) r is critical and q is subcritical;(iii) r is subcritical and q is critical;(iv) Both q and r are critical.