In this paper, we study the existence and asymptotic behavior of nodal solutions to the following Kirchhoff problem -(a+b integral(3)(R)vertical bar del u vertical bar(2)dx)Delta u + v(vertical bar x vertical bar)u = f(vertical bar x vertical bar, u), in R-3 , u is an element of H-1(R-3), where V(x) is a smooth function, a, b are positive constants. Because the so-called nonlocal term (integral(3)(R)vertical bar del u vertical bar(2)dx)Delta u)Au is involved in the equation, the variational functional of the equation has totally different properties from the case of b = 0. Under suitable const...
