Existence Results for Superlinear Elliptic Equations with Nonlinear Boundary Value Conditions  

作　　者：Xiao Hui YU 

机构地区：[1]College of Mathematics and Statistics, Shenzhen University

出　　处：《Acta Mathematica Sinica,English Series》2019年第10期1655-1680,共26页数学学报（英文版）

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

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.In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition■ 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.

关 键 词：Existence result critical EXPONENT trace INEQUALITY NONLINEAR boundary value (PS) condition 

分 类 号：O1[理学—数学]