数学物理学报(英文版) ›› 2000, Vol. 20 ›› Issue (3): 374-379.

• 论文 • 上一篇    下一篇

MULTIPLE SOLUTIONS OF NONHOMOGENEOUS FOR RELATED CHOQUARD’S EQUATION

 张正杰   

  1. Department of Mathematics, Huazhong Normal University, Wuhan 430079, China
  • 收稿日期:1998-10-27 修回日期:1999-08-16 出版日期:2000-05-20 发布日期:2000-05-20
  • 基金资助:

    Supported by Young Teacher Fundation. NECC.

MULTIPLE SOLUTIONS OF NONHOMOGENEOUS FOR RELATED CHOQUARD’S EQUATION

 ZHANG Zheng-Jie   

  1. Department of Mathematics, Huazhong Normal University, Wuhan 430079, China
  • Received:1998-10-27 Revised:1999-08-16 Online:2000-05-20 Published:2000-05-20
  • Supported by:

    Supported by Young Teacher Fundation. NECC.

摘要:

his paper considers the existence of solutions for the following problem:
−u + u + v(x)u = (|u|2 ∗
1
|x|
)u + g(x), x ∈ R3
where v(x) be a continuous function on R3,v(x) < 0, v(x) −→ 0, (as |x| −→ ∞); g(x) ≥
0, g(x) 6≡ 0 and g(x) ∈ H−1(R3). The author proves that there exists a constant C, such
that kg(x)kH−1 ≤ C,then there are at least two solutions for the above problem.

关键词: Multiple solutions, existence, Choquard’s equation

Abstract:

his paper considers the existence of solutions for the following problem:
−u + u + v(x)u = (|u|2 ∗
1
|x|
)u + g(x), x ∈ R3
where v(x) be a continuous function on R3,v(x) < 0, v(x) −→ 0, (as |x| −→ ∞); g(x) ≥
0, g(x) 6≡ 0 and g(x) ∈ H−1(R3). The author proves that there exists a constant C, such
that kg(x)kH−1 ≤ C,then there are at least two solutions for the above problem.

Key words: Multiple solutions, existence, Choquard’s equation

中图分类号: 

  • 35J60