Positive radial solutions for the problem with Minkowski-curvature operator on an exterior domain

We are concerned with the problem with Minkowski-curvature operator on an exterior domain ⎨ ⎪ ⎪⎪⎪⎧ ⎪⎪⎪⎪⎩ ) -div( backward difference u & RADIC;1-| backward difference u|2 = & lambda;K(| x|) f(u) u & gamma;in Bc , partial differential u partial differential n| partial differential Bc = 0 , lim |x|& RARR;& INFIN;u(x) = 0 , (P) where 0 & LE; & gamma; < 1, Bc = {x & ISIN; RN : |x| > R} is a exterior domain in RN , N > 2, R > 0, K & ISIN; R & INFIN; C([R , & INFIN;) , (0 , & INFIN;)) is such that R rK(r)dr < & INFIN;, the function f : [0 , & INFIN;) & RARR; (0 , & INFIN;) is a continuous function such that lim s & RARR;& INFIN; positive radial solution for all & lambda; > 0. The proof of our main result is based upon the method of sub and super solutions. f (s) s & gamma;+1 = 0 and & lambda; > 0 is a parameter. We show that problem (P) has at least one