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Ground state and nodal solutions for a class of biharmonic equations with singular potentials |
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| Authors: | Hongliang Liu Qizhen Xiao Hongxia Shi Haibo Chen Zhisu Liu |
| Affiliation: | School of Mathematics and Physics, University of South China, Hengyang, 421001, China,School of Mathematics and Physics, University of South China, Hengyang, 421001, China,School of Mathematics and Physics, University of South China, Hengyang, 421001, China,Shool of Mathematics and Statistics, Central South University, Changsha, 410083, China and School of Mathematics and Physics, University of South China, Hengyang, 421001, China |
| 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. |
| Keywords: | Biharmonic equation ground state and nodal solution variational methods Hessian matric energy doubling. |
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