EXISTENCE AND NONEXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF p-LAPLACIAN SUPERLINEAR PROBLEMS WITH NONLINEAR BOUNDARY CONDITIONS

We prove the existence of positive radial solutions to the problem {-Delta(p)u =lambda K(vertical bar x vertical bar) f(u) in vertical bar x vertical bar > r(0), partial derivative u/partial derivative n + (c) over tilde (u)u = 0 on vertical bar x vertical bar =r(0), u(x) -> 0 as vertical bar x vertical bar -> infinity, where Delta(u)(p) = div(vertical bar del u vertical bar(p-2)del u), N > p > 1,Omega = {x is an element of R-N : vertical bar x vertical bar > r(0) > 0 }, f : (0, infinity) -> R is p-superlinear at infinity with possible singularity at 0, and lambda is a small positive parameter. A nonexistence result is also established when f has semipositone structure at 0.