带有Hardy和临界指标项的非齐次椭圆方程的解
On Nonhomogeneous Elliptic Problems Involving Hardy Potential and Critical Sobolev Exponent
摘要
考虑了带有Hardy和临界指标项的非齐次椭圆方程,当非齐次项f满足特定的条件时,得到了方程有两个正解.
The Schr？dinger equations with Hardy potential and critical Sobolev exponent are concerned.Under appropriate assumptions,then equation admits at least two solutions.
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
2016年第3期25-32,共8页
Acta Scientiarum Naturalium Universitatis Nankaiensis
关键词
非齐次
临界指标
正解
nonhomogeneous
critical Sobolev exponent
positive solution
参考文献9
-
1Cao D M, Peng S J. A note on the sign-changing solution to elliptic problems with critical Sobolev and Hardy terms[J]. J Differential Equations, 2003, 193: 424-434.
-
2Chen Z J, Zou W M. On an elliptic problem with critical exponent and Hardy potential[J]. J Differential Equa- tions,2012, 252: 969-987.
-
3Tarantello G. On nonhomogeneous elliptic problems involving critical Sobolev exponent[J]. Ann Inst H Poincar Analyse Non Linaire, 1992, 9: 281--304.
-
4Wang Z P, Zhou H S. Solutions for a nonhomogeneous nent in RN [J]. Acta Mathematica Scientia, 2006, 26B(3) elliptic problem involving critical Sobolev-Hardy expo- 525--536.
-
5Catrina F, Wang Z Q. On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexis- tence),and symmetry of extermal functions[J]. Comm Pure Appl Math, 2001, 54: 229-258.
-
6Aubin J P, Ekeland I. Applied Nonlinear Analysis, Pure and Applied Mathematic[Ml. [S.1.]: Wiley, 1984.
-
7Cao D M, Zhou H S. Multiple poitive solutions of nonhomogeneous semilinear elliptic equations in RN [J]. Pro- ceedings of the Royal Society of Edinburgh, 1996, 126A: 443-463.
-
8Brezis H, Lieb E. A relation between pointwise convergence of functions and convergence of integrals[J]. Proc Amer[J]. Math Soc, 1983, 88: 486--490.
-
9Deng Y B, Jin L Y, Peng S J. Solutions of Schrodinger equations wih invere square potential and critical non- linearity[J]. J Differemial Equations, 2012, 252:1 376-1 398.
-
1杨芬,胡松.全空间上一类非齐次椭圆方程正解的衰减[J].数学杂志,2015,35(6):1469-1474.
-
2佟玉霞,金殿川,谷建涛.关于障碍问题很弱解的注记[J].宁夏大学学报（自然科学版）,2009,30(3):217-219.
-
3樊自安.包含Caffarelli-Kohn-Nirenberg临界指数的非齐次椭圆方程[J].数学物理学报（A辑）,2015,35(5):884-894.
-
4刘保相,谷建涛.椭圆方程双侧障碍问题解的局部有界性[J].应用数学,2012,25(1):90-95. 被引量：1
-
5张靖.带有Sobolev临界指标项的非齐次椭圆方程的解[J].应用数学,2016,29(2):388-397.
-
6佟玉霞,徐秀娟,安敏,谷建涛.非齐次椭圆方程障碍问题的很弱解[J].河北理工大学学报（自然科学版）,2007,29(3):102-104.
-
7张靖,马世旺.带有Sobolev-Hardy临界指标项的非齐次椭圆方程的解[J].数学学报（中文版）,2017,60(2):201-216.
-
8邓志颖,黄毅生.具Hardy-Sobolev临界指数的非齐次椭圆方程的正解[J].应用数学学报,2009,32(6):1104-1122. 被引量：1
-
9樊自安.非齐次椭圆型方程双侧障碍问题的很弱解[J].湖北工程学院学报,2016,36(6):122-124.
-
10谢华朝,李素丽.一类非齐次临界椭圆方程在RN中的正解[J].数学物理学报（A辑）,2013,33(6):1099-1111.
