Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN

Abstract EN

The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter λ on RN is proved by using variational method.

We will show that if the nonlinearities are asymptotically linear at infinity and λ>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.