Multiple solutions for the asymptotically linear Kirchhoff type equations on \(\mathbb{R}^N\) (Q341222)

Summary: The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter \(\lambda\) on \(\mathbb{R}^N\) is proved by using variational methods. We show that if the nonlinearities are asymptotically linear at infinity and \(\lambda > 0\) is sufficiently small, the Kirchhoff type equations have at least two positive solutions. For the perturbed problem, we give the result of existence of three positive solutions.