| Volume 9, Number 4, 2019, Pages 1393-1406 DOI：10.11948/2156-907X.20180253 |
| Ground state and nodal solutions for a class of biharmonic equations with singular potentials |
| Hongliang Liu,Qizhen Xiao,Hongxia Shi,Haibo Chen,Zhisu Liu |
| Keywords:Biharmonic equation, ground state and nodal solution, variational methods, Hessian matric, energy doubling. |
| 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. |
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