数学物理学报(英文版) ›› 1992, Vol. 12 ›› Issue (3): 292-303.

• 论文 • 上一篇    下一篇

POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

薛儒英   

  1. Dept. of Math., Hangzhou Univ., Hangzhou 310028, China
  • 收稿日期:1990-01-15 出版日期:1992-09-25 发布日期:1992-09-25
  • 基金资助:
    Project supported by the Natural Science Foundation of Zhejiang Province.

POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

Xue Ruying   

  1. Dept. of Math., Hangzhou Univ., Hangzhou 310028, China
  • Received:1990-01-15 Online:1992-09-25 Published:1992-09-25
  • Supported by:
    Project supported by the Natural Science Foundation of Zhejiang Province.

PDF (PC)

27

摘要： We consider the nonlinear elliptic equation with mixed boundary conditions
(P)-△u=b(x)up+λu,u>0 for x∈Ω,u|Γ0=0,(∂u)/∂n|Γ1=0, where Ω is a smooth bounded domain in RN (N ≥ 3), whose boundary ∂Ω is made of two open sets Γ0 and Γ1,Γ0∩Γ1=ϕ, ∂Ω=Γ0∪Γ1,p=(N+2)/N-2. We prove the existence of a positive solution of (P)when b (x) and λ satisfy suitable conditions.

Abstract: We consider the nonlinear elliptic equation with mixed boundary conditions
(P)-△u=b(x)up+λu,u>0 for x∈Ω,u|Γ0=0,(∂u)/∂n|Γ1=0, where Ω is a smooth bounded domain in RN (N ≥ 3), whose boundary ∂Ω is made of two open sets Γ0 and Γ1,Γ0∩Γ1=ϕ, ∂Ω=Γ0∪Γ1,p=(N+2)/N-2. We prove the existence of a positive solution of (P)when b (x) and λ satisfy suitable conditions.

版权所有 © 《数学物理学报(英文版)》杂志社
地址：武汉市71010号信箱(430071)　电话: 027-87199206(中文版)　027-87199087(英文版)
E-mail: actams@apm.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发