On the effect of space dimension and potential on the multiplicity of positive and nodal solutions for Kirchhoff equations

The paper is concerned with the multiplicity of positive and nodal solutions for the following Kirchhoff equation arising in the study of string or membrane vibrations−(a+b∫RN|∇u|2dx)Δu+λV(x)u=|u|p−2u,inRN, where N≥3, a,b and λ are positive parameters, the potential V(x)∈C(RN,R+), and 2