A Class of Quasilinear Dirichlet Problems with Unbounded Coefficients and Singular Quadratic Lower Order Terms

Abstract

We study existence and regularity of positive solutions of problems like $$\left\{\begin{array}{cl} - {\rm div}([a(x) + u^q] \nabla u) + b(x)\frac{1}{u^\theta}|\nabla u|^2 = f & {\rm in} \, \Omega,\\ u > 0 &{\rm in} \, \Omega, \\ u = 0 & {\rm on} \, \partial\Omega ,\end{array}\right.$$ depending on the values of q > 0, 0 < θ < 1, and on the summability of the datum f ≥ 0 in Lebesgue spaces.