Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1634-1645.
Previous Articles Next Articles
Multiple Positive Solutions for a Quasilinear Elliptic System Involving the Caffarelli-Kohn-Nirenberg Inequality and Nonlinear Boundary Conditions
Qin Li1(
),Zuodong Yang2,*()
- 1 School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Anhui Bengbu 233030
2 School of Teacher Education, Nanjing University of Information Science and Technology, Nanjing 210044
-
Received:2019-08-12Online:2020-12-26Published:2020-12-29 -
Contact:Zuodong Yang E-mail:liqin_math@163.com;zdyang_jin@263.net -
Supported by:the Anhui Natural Science Foundation(1808085QA15);the Scientific Research Project of Anhui University of Finance and Economics(ACKYC19050);the NSFC(11571093)
CLC Number:
- O175.2
Cite this article
Qin Li,Zuodong Yang. Multiple Positive Solutions for a Quasilinear Elliptic System Involving the Caffarelli-Kohn-Nirenberg Inequality and Nonlinear Boundary Conditions[J].Acta mathematica scientia,Series A, 2020, 40(6): 1634-1645.
share this article
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| 1 | Abdellaoui B , Colorado E , Peral I . Some critical quasilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions:relation with Sobolev and Sobolev-Hardy optimal constants. J Math Anal Appl, 2007, 332: 1165- 1188 |
| 2 | Brezis H , Lieb E . A relation between pointwise convergence of functions and convergence of functions. Proc Amer Math Soc, 1983, 88: 486- 490 |
| 3 | Caffarelli L , Kohn R , Nirenberg L . First order interpolation inequalities with weights. Compos Math, 1984, 53: 259- 275 |
| 4 | Drabek P , Pohozaev S . Positive solutions for the p-Laplacian:Application of the fibering method. Proc Roy Soc Edinburgh Sect A, 1997, 127: 703- 726 |
| 5 | Felli V , Schneider M . Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type. J Differ Equ, 2003, 191: 121- 142 |
| 6 | Huang X , Wu X , Tang C . Multiple positive solutions for semilinear elliptic equations with critical weighted Hardy-Sobolev exponents. Nonlinear Anal, 2011, 74: 2602- 2611 |
| 7 | Horiuchi T . Best constant in weighted Sobolev inequality with weights being powers of distance from the origin. J Inequal Appl, 1997, 1: 275- 292 |
| 8 | Kang D . On elliptic problems with critical weighted Sobolev-Hardy exponents. Nonlinear Anal, 2007, 66: 1037- 1050 |
| 9 | Benmansour S , Matallah A . Multiple solutions for nonhomogeneous elliptic equations involving critical Caffarelli-Kohn-Nirenberg exponent. Mediterr J Math, 2016, 13: 4679- 4691 |
| 10 | Lü D , Xiao J . Multiple solutions for weighted nonlinear elliptic system involving critical exponents. Math Comput Modelling, 2012, 55: 816- 827 |
| 11 | Kang D , Kang Y . Quasilinear elliptic systems involving critical Hardy-Sobolev and Sobolev exponents. Bull Malays Math Sci Soc, 2017, 40: 1- 17 |
| 12 | Li G , Peng S . Remarks on elliptic problems involving the Caffarelli-Kohn-Nirenberg inequalities. Proc Amer Math Soc, 2008, 136: 1221- 1228 |
| 13 | Nyamoradi N , Shekarbigi M . Existence of positive solutions for a quasilinear elliptic system involving critical Sobolev-Hardy exponents and concave-convex nonlinearities. Arab J Math, 2013, 2: 365- 379 |
| 14 | Nyamoradi N. A variational approach to a singular elliptic system involving critical Sobolev-Hardy exponnets and concave-convex nonlinearities. Math Sci, 2013, 7, Article number: 11 |
| 15 | Nyamoradi N , Hsu T . Existence of multiple positive solutions for semilinear elliptic systems involving m critical Hardy-Sobolev exponents and m sign-changing weight function. Acta Math Sci, 2014, 34B (2): 483- 500 |
| 16 | Secchi S , Smets D , Willem M . Remarks on a Hardy-Sobolev inequality. C R Acad Sci Paris, 2003, 336: 811- 815 |
| 17 | Talenti G . Best constant in Sobolev inequality. Ann Mat Pur Appl, 1976, 110: 353- 372 |
| 18 | Wang L . Multiple solutions for a class of concave-convex quasilinear elliptic systems with nonlinear boundary condition. Appl Math, 2013, 4: 449- 455 |
| 19 | Xiu Z , Chen C , Huang J . Existence of multiple solutions for an elliptic system with sign-changing weight functions. J Math Anal Appl, 2012, 395: 531- 541 |
| 20 | Kang D . Positive solutions to the weighted critical quasilinear problems. Appl Math Comput, 2009, 213: 432- 439 |
| 21 | Xiu Z , Chen C . Existence of multiple solutions for singular elliptic problems with nonlinear boundary conditions. J Math Anal Appl, 2014, 410: 625- 641 |
| 22 | Li Y , Gao W . Existence of multiple solutions for singular quasilinear elliptic system with critical Sobolev-Hardy exponents and concave-convex terms. Acta Math Sci, 2013, 33B (1): 107- 121 |
| [1] | Yan Luo,Wenzhe Xie. Existence of Solutions for Impulsive Differential Inclusions with Upper and Lower Solutions in the Reverse Order [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1055-1063. |
| [2] | Liwan Fang,Wennian Huang,Minqing Wang. Ground-State Solutions for Schrödinger-Maxwell Equations in the Critical Growth [J]. Acta mathematica scientia,Series A, 2019, 39(3): 475-483. |
| [3] | Ting Ji,Lianggen Hu,Jing Zeng. The Non-Existence of Non-Radial Blow-Up Solutions for the Quasilinear Elliptic System [J]. Acta mathematica scientia,Series A, 2019, 39(2): 307-315. |
| [4] | Yu Chun, Wan Youyan. The Existence of Ground State to the Generalized Choquard-Pekar Equation with Superlinear Nonlinearities [J]. Acta mathematica scientia,Series A, 2018, 38(2): 276-283. |
| [5] | Chen Lin. Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type [J]. Acta mathematica scientia,Series A, 2017, 37(4): 671-683. |
| [6] | Qin Dongdong, Li Yunyang, Tang Xianhua. Schrödinger Equation with Asymptotically Linear Nonlinearity and Spectrum Point Zero [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1103-1116. |
| [7] | Li Jing, Chen Caisheng. Nehari Method to Solutions for a Class of Quasilinear Schrödinger Equations in RN [J]. Acta mathematica scientia,Series A, 2016, 36(3): 507-520. |
| [8] | Li Qin, Yang Zuodong. Multiple Solutions for a Class of Quasilinear Nonhomogeneous Elliptic Systems with Nonlinear Boundary Conditions [J]. Acta mathematica scientia,Series A, 2016, 36(2): 307-316. |
| [9] | Fan Zi-an. On Nonhomogeneous Elliptic Equations Involving Caffarelli-Kohn-Nirenberg Critical Exponent [J]. Acta mathematica scientia,Series A, 2015, 35(5): 884-894. |
| [10] | ZHANG Wen-Li, ZHONG Li-Nan. Multiplicity of Positive Solutions for a (p, q-Laplacian Elliptic Systems in RN [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1264-1274. |
| [11] | ZHANG Jian, TANG Xian-Hua, ZHANG Wen. ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION [J]. Acta mathematica scientia,Series A, 2014, 34(3): 840-850. |
| [12] | ZHANG Shu-Tao. Weighted Hardy-Sobolev Inequality and Its Application [J]. Acta mathematica scientia,Series A, 2013, 33(4): 621-626. |
| [13] | PENG Yan-Fang, WANG Ji-Xiu. Multiplicity of Solutions for a Singular Equation [J]. Acta mathematica scientia,Series A, 2013, 33(4): 766-776. |
| [14] | ZHANG Ya-Jing. Multiple Solutions for Biharmonic Equations with Concave-Convex Nonlinearities [J]. Acta mathematica scientia,Series A, 2013, 33(2): 353-365. |
| [15] | ZHANG Wen-Li, ZHONG Li-Nan. Existence and Multiplicity of Nonnegative Solutions for a Quasilinear System in RN [J]. Acta mathematica scientia,Series A, 2013, 33(1): 174-184. |
|