The Existence of Multiple Solutions for Nonhomogeneous Kirchhoff Type Equations in ℝ3

Abstract EN

We are concerned with the existence of multiple solutions to the nonhomogeneous Kirchhoff type equation -(a+b∫ℝ3|∇u|2)Δu+u=|u|p-1u+h(x) in ℝ3, where a, b are positive constants, p∈(1,5), 0⩽h(x)=h(|x|)∈C1(ℝ3)∩L2(ℝ3), we can find a constant mp>0 such that for all p∈(1,5) the equation has at least two radial solutions provided |h|2