JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 75-80.doi: 10.6040/j.issn.1671-9352.0.2018.496

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Uniqueness of positive solutions of singular p-biharmonic equations with Hardy terms

  

  1. School of Science, North University of China, Taiyuan 030051, Shanxi, China
  • Published:2019-06-05

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Abstract: We study a class of singular p-biharmonic equations with Hardy terms. The existence and uniqueness of the positive solution for above problem is obtained by minimization method.

Key words: Hardy terms, singular p-biharmonic equations, minimization method, positive solution, existence and uniqueness

CLC Number: 

  • O175.25
[1] PERERA K, SILVA E A B. Existence and multiplicity of positive solutions for singular quasilinear problems[J]. Journal of Mathematical Analysis and Applications, 2006, 323(2):1238-1252.
[2] ZHAO L, HE Y, ZHAO P. The existence of three positive solutions of a singular p-Laplacian problem[J]. Nonlinear Analysis, 2011, 74(16):5745-5753.
[3] BUENO H, PAES-LEME L, RODRIGUES H C. Multiplicity of solutions for p-biharmonic problems with critical growth[J]. Rocky Mountain J Math, 2018, 48:425-442.
[4] CHEN Q, CHEN C. Infinitely many solutions for a class of p-biharmonic equation in RN[J]. Bull Iranian Math Soc, 2017, 43(1):205-215.
[5] 廖家锋, 陈明, 张鹏. 一类奇异共振椭圆方程正解的唯一性[J]. 数学杂志, 2017, 37(3):513-518. LIAO Jiafeng, CHEN Ming, ZHANG Peng. Uniqueness of positive solutions for a class of singular resonance elliptic equations[J]. Journal of Mathematics, 2017, 37(3):513-518.
[6] 廖家锋, 李红英, 段誉. 一类奇异p-Laplacian方程正解的唯一性[J]. 西南大学学报(自然科学版), 2016, 38(6):45-49. LIAO Jiafeng, LI Hongying, DUAN Yu. Uniqueness of positive solutions for a class of singular p-Laplacian equations[J]. Journal of Southwest University(Natural Science Edition), 2016, 38(6):45-49.
[7] 李红英, 佘连兵, 廖家锋. 一类奇异p-Laplace方程正解的存在性[J]. 西北师范大学学报(自然科学版), 2016, 52(4):1-4. LI Hongying, SHE Lianbing, LIAO Jiafeng. Uniqueness of positive solutions for a class of singular p-Laplace equations[J]. Journal of Northwest Normal University(Natural Science Edition), 2016, 52(4):1-4.
[8] 唐榆婷, 唐春雷. 一类带Hardy-Sobolev临界指数的Kirchhoff方程正解的存在性[J]. 西南大学学报(自然科学版), 2017, 39(6):81-86. TANG Yuting, TANG Chunlei. Existence of positive solutions for a class of Kirchhoff equations with Hardy-Sobolev critical exponents[J]. Journal of Southwest University(Natural Science Edition), 2017, 39(6):81-86.
[9] YANG Ruirui, ZHANG Wei, LIU Xiangqing. Sign-changing solutions for p-biharmonic equations with Hardy potential in RN[J]. Acta Mathematica Scientia, 2017, 37B(3):593-606.
[10] LIAO Jiafeng, KE Xiaofeng, LEI Chunyu, et al. A uniqueness result for Kirchhoff type problems with singularity[J]. Applied Mathematics Letters, 2016, 59:24-30.
[11] HUANG Yisheng, LIU Xiangqing. Sign-changing solutions for p-biharmonic equationswith Hardy potential[J]. Journal of Mathematical Analysis and Applications, 2014, 412(3):142-154.
[12] DAVIES E B, HINZ A M. Explicit constants for Rellich inequalities[J]. Mathematische Zeitschrift, 1998, 227(3):511-523.
[13] RUDIN W. Real and complex analysis[M]. New York: McGraw-Hill, 1986.
[14] BRÉZIS H, LIEB E. A relation between pointwise convergence of functions and convergence of functionals[J]. Proceedings of the American Mathematical Society, 1983, 88(3):486-490.
[15] SUN Y J, WU S, LONG Y. Combined effects of singular and superlinear nonlinearities in some singular boundary value problems[J]. Journal of Differential Equations, 2001, 176(2):511-531.
[16] VÁZQUEZ J L. A strong maximum principle for some quasilinear elliptic equations[J]. Applied Mathematics and Optimization, 1984, 12(1):191-202.
[17] LINDQVIST Peter. On the equation div(|∇u|p-2∇u)+λup-2u=0[J]. Proceedings of the American Mathematical Society, 1992, 116(2):583-584.
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