We consider a nonlinear elliptic equation of the formdiv [a(∇u)] + F[u] = 0on a domain Ω, subject to a Dirichlet boundary conditiontru = φ. We do not assume that the higher order terma satisfies growth conditions from above. We prove the existence ofcontinuous solutions either when Ω is convex and φ satisfies a one-sidedbounded slope condition, or when a is radial:\hbox{$a(\xi)=\fr{l(|\xi|)}{|\xi|} \xi$} for some increasingl:ℝ+ → ℝ+.