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 Δ U(x)+φ(|x|)f(U)=0 with a nonlinear boundary conditions on exterior of the unite ball centered at the origin in RN 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,β), $ f0$ on (β,∞). The function φ0 is C¹ on [R,∞) where 0φ(|x|)≤ c₀\,|x|-α with α2(N-1) and $ N2 $ for large $ |x| $.