Azer Sign-changing radial solutions for a semilinear problem on exterior domains with nonlinear boundary conditions

In this paper we are interested to the existence and multiplicity of sign changing radial solutions of problem of elliptic equations U (x) + (|x|) f (U) =0 with a nonlinear boundary conditions on exterior of the unite ball centered at the origin in R^N such that u (x) 0 as |x|, with any given number of zeros where the nonlinearity f (u) is odd, superlinear for u lager enough and f0 on (0, ), f0 on (, ). The function 0 is C^1 on [R, ) where 0 (|x|) c₀\, |x|^- with 2 (N-1) and N2 for large |x|.