Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN - Yu Duan; Chun-Lei Tang (International Journal of Differential Equations)
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.