Abstract
In this paper, we consider the following Kirchhoff equation in R3 with critical growth. (a+b∫R3|∇u|2dx)Δu−V(x)u+u5+μ|u|q−2u=0,inR3,u(x)→0,as|x|→∞,where V is the potential function, a,b,μ>0,5<q<6 are constants. We assume V is a radial function and is bounded from below by a positive constant. We prove that for any given positive integer k, the problem has a radial solution, having k nodal domains exactly.
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