GROUND STATE AND NODAL SOLUTIONS FOR A CLASS OF BIHARMONIC EQUATIONS WITH SINGULAR POTENTIALS

Hongliang Liu; Qizhen Xiao; Hongxia Shi; Haibo Chen; Zhisu Liu

doi:10.11948/2156-907X.20180253

2019 Volume 9 Issue 4

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Hongliang Liu, Qizhen Xiao, Hongxia Shi, Haibo Chen, Zhisu Liu. GROUND STATE AND NODAL SOLUTIONS FOR A CLASS OF BIHARMONIC EQUATIONS WITH SINGULAR POTENTIALS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1393-1406. doi: 10.11948/2156-907X.20180253

Citation:

Hongliang Liu, Qizhen Xiao, Hongxia Shi, Haibo Chen, Zhisu Liu. GROUND STATE AND NODAL SOLUTIONS FOR A CLASS OF BIHARMONIC EQUATIONS WITH SINGULAR POTENTIALS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1393-1406. doi: 10.11948/2156-907X.20180253

GROUND STATE AND NODAL SOLUTIONS FOR A CLASS OF BIHARMONIC EQUATIONS WITH SINGULAR POTENTIALS

1.
School of Mathematics and Physics, University of South China, Hengyang, 421001, China
2.
School of Mathematics and Computational Science, Hunan First Normal University, Changsha, 410205, China
3.
School of Mathematics and Statistics, Central South University, Changsha, 410083, China

Corresponding author: Email address:math_lhliang@163.com(H. Liu)
Fund Project: The authors were supported by the Hunan Natural Science Fund Youth Fund Project(No. 2018JJ3419), Scientific Research Fund of Hunan Provincial Education Department(Nos. 17C1362 and 17C1364) and Doctoral Funds of SCU(Nos. 2016XQD40 and 2016XQD42)

Abstract

Abstract

In this paper, we are concerned with a class of fourth order elliptic equations of Kirchhoff type with singular potentials in $ \mathbb{R}^{N}. $ The existence of ground state and nodal solutions are obtained by using variational methods and properties of Hessian matric. Furthermore, the "energy doubling" property of nodal solutions is also explored.
- Biharmonic equation /
- ground state and nodal solution /
- variational methods /
- Hessian matric /
- energy doubling
MSC: 35J35, 35J75, 35B33

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References

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