|
|
- 2018
一类带双临界指数的Schr？dinger-Poisson系统正基态解的存在性
|
Abstract:
利用变分法和山路引理研究一类带有双临界指数的Schr？dinger-Poisson系统,证明了其正基态解的存在性.
By using the variational method and the mountain pass theorem, we prove the existence of positive ground state solutions for a class of Schr？dinger-Poisson systems with double critical exponents
| [1] | AZZOLLINI A, D'AVENIA P, LUISI V. Generalized Schr？dinger-Poisson Type Systems[J]. Commun Pur Appl Anal, 2017, 12(2): 867-879. |
| [2] | LI F Y, LI Y H, SHI J P. Existence of Positive Solutions to Schr？dinger-Poisson Type Systems with Critical Exponent[J]. Commun Contemp Math, 2014, 16(6): 1-28. |
| [3] | 李苗苗, 唐春雷. 一类带临界指数的Schr？dinger-Poisson方程正解的存在性[J]. 西南师范大学学报(自然科学版), 2016, 41(4): 35-38. |
| [4] | BENCI V, FORTUNATO D. An Eigenvalue Problem for the Schr？dinger-Maxwell Equations[J]. Topol Methods Nonlinear Anal, 1998, 11(2): 283-293. DOI:10.12775/TMNA.1998.019 |
| [5] | ZHONG X J, TANG C L. Ground State Sign-Changing Solutions for a Schr？dinger-Poisson System with a Critical Nonlinearity in ${{\mathbb{R}}^{3}}$ [J]. Nonlinear Anal, 2018, 39(2): 166-184. |
| [6] | ZHAO L G, ZHAO F K. Positive Solutions for Schr？dinger-Poisson Equations with a Critical Exponent[J]. Nonlinear Anal, 2009, 70(6): 2150-2164. DOI:10.1016/j.na.2008.02.116 |
| [7] | WILLEM M. Minimax Theorems[M]. Boston: Birkh？user, 1996. |
| [8] | JEANJEAN L. Existence of Solutions with Prescribed Norm for Semilinear Elliptic Equations[J]. Nonlinear Anal, 1997, 28(10): 1633-1659. DOI:10.1016/S0362-546X(96)00021-1 |
| [9] | BRéZIS H, NIRENBERG L. Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents[J]. Commun Pure Appl Math, 1983, 36(4): 437-477. DOI:10.1002/(ISSN)1097-0312 |
