Abstract
In the present paper, we consider the following Kirchhoff type problem −(a+b∫R3|∇u|2dx)Δu+V(x)u=f(u)inR3,where a,b>0 and the potential V has double potential well. With an asymptotically 4-linear nonlinearity f, we prove that the Kirchhoff type problem has one least energy nodal solution by variational methods.
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