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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 $\mathbf{R}^{N}.$ 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.