EXISTENCE OF POSITIVE ENTIRE SOLUTIONS OF A SEMILINEAR p–LAPLACIAN PROBLEM WITH A GRADIENT TERM

In this paper, we study a semilinear p -Laplacian problem −Δpu+h(x)|∇u| = b(x)g(u), u > 0, x ∈ R , lim |x|→∞ = 0, where q ∈ (p− 1, p], b, h ∈Cα loc(R) for some α ∈ (0,1), h(x) 0, b(x) > 0,∀x ∈ RN , and g ∈ C1((0,∞),(0,∞)) which may be singular at 0 . Using a sub-supersolution argument and a perturbed argument, we obtain the existence of entire solutions to the problem. No monotonicity condition is imposed on the functions g(s) and g(s) sp−1 . Mathematics subject classification (2010): 35J61, 35J91.