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

We are concerned with the existence of multiple solutions to the nonhomogeneous Kirchhoff type equation -(a+b integral(R3) vertical bar del u vertical bar(2))Delta u+u = |u|(p-1)u + h(x) in R-3, where a, b are positive constants, p epsilon (1, 5), 0 <= h (x) = h(vertical bar x vertical bar) epsilon C-1 (R-3) boolean AND L-2 (R-3), we can find a constant m(p) > 0 such that for all p epsilon (1,5) the equation has at least two radial solutions provided vertical bar h vertical bar(2) < m(p).