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- 2018
带有加权Hardy-Sobolev临界指数的拟线性椭圆方程正解的存在性和多重性
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Abstract:
研究了一类加权拟线性椭圆方程,利用Ekeland变分原理和强极大值原理,证明了该方程正解的存在性和多重性.
We investigate a quasilinear elliptic equation with weighted Hardy-Sobolev exponents and, by means of Ekeland's variational principle and strong maximum principle, prove the existence and multiplicity of its positive solutions under different conditions
[1] | GHOUSSOUB N, YUAN C. Multiple Solutions for Quasi-Linear PDEs Involving the Critical Sobolev and Hardy Exponents[J]. Trans Amer Math Soc, 2000, 352(12): 5703-5743. DOI:10.1090/S0002-9947-00-02560-5 |
[2] | PENG Z, CHEN G. Existence and Multiplicity of Positive Solutions for P-Laplacian Elliptic Equations[J]. Bound Value Probl, 2016, 2016: 125. DOI:10.1186/s13661-016-0632-5 |
[3] | KANG D. Positive Solutions to the Weighted Critical Quasilinear Problems[J]. Appl Math Comput, 2009, 213(2): 432-439. |
[4] | KANG D. Some Results on Weighted Critical Quasilinear Problems[J]. Differ Equ Appl, 2010, 2(4): 519-535. |
[5] | 刘海燕, 廖家锋, 唐春雷. 带Hardy-Sobolev临界指数的半线性椭圆方程正解的存在性[J]. 西南大学学报(自然科学版), 2015, 37(6): 60-65. |
[6] | 丁凌, 唐春雷. 具有Hardy-Sobolev临界指数的p-Laplacian方程解的存在性和多重性[J]. 西南大学学报(自然科学版), 2007, 29(4): 5-10. |
[7] | BREZIS H, NIRENBERG L. Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents[J]. Comm Pure Appl Math, 1983, 36(4): 437-477. DOI:10.1002/(ISSN)1097-0312 |
[8] | KANG D. Some Properties of Solutions to the Singular Quasilinear Problems[J]. Nonlinear Anal, 2010, 72(2): 682-688. DOI:10.1016/j.na.2009.07.009 |