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In this paper, we are concerned with nodal solutions for a class of Kirchhoff-type problemswhere,  a ,  b &gt;0,  f  satisfies some asymptotically linear growth conditions. First of all, when  N  = 3,  b &gt;0 and,  b &gt;0 sufficiently small, we attain infinitely many nodal solutions by an equivalent transformation. Based on this, via a new and direct approach, the least energy sign-changing radial solutions can be obtained for the above problem. What's more, we also establish non-existence results of nodal solutions forand  b  large enough.

Nodal solutions for an asymptotically linear Kirchhoff-type problem in ℝ N