Existence and asymptotic behavior of solutions for a class of nonlinear elliptic equations with Neumann condition

In this paper, we study the existence of nonconstant solutions uε and their asymptotic behavior (as ε→0+) for the following class of nonlinear elliptic equations in radial form:-ε2(rα|u′|βu′)′=rγf(u)in (0,R),u′(0)=u′(R)=0,where α,β,γ are given real numbers and 0