Multiple Solutions for the Asymptotically Linear Kirchhoff Type Equations on RN

[摘要] The multiplicity of positive solutions for Kirchhoff type equations depending on a nonnegative parameter ? on RN is proved by using variational method. We will show that if the nonlinearities are asymptotically linear at infinity and ?>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.

[学科分类] 几何与拓扑