With The Convection Term For A Class Of Linear Elliptic Equations Of The Existence Of Positive Entire Solutions

By a sub-supersolution method, a perturbation argument and the maximum princi-ple, combining with the theory of estimates and regularity of second order linear ellipticdifferential equations, we study the following nonlinear elliptic problems:Here, N≥1, q∈(0,2],λ∈R andλ≠0. Also we assume that g∈C¹((0,∞),(0,∞))satisfying lim_uâ†'0+ g(u)/u= +∞and lim_{uâ†'∞} g(u)/u= 0, f : [0,∞)â†'[0,∞) is locallyH(o|¨)lder continuous and satisfies lim_uâ†'0+ f(u)/u= +∞and lim_{uâ†'∞} f(u)/u= 0. Moreover,p∈C_loc^α(R^N) (α∈(0,1)) and p(x) > 0, (?) x∈R^N.We respectively show the existence of positive entire solutions for the above nonlin-ear elliptic problem in two cases:λ> 0 andλ< 0.