The authors investigate the existence of positive solutions of the Dirichlet problem
in convex bounded domains , where are nondecreasing continuously differentiable functions. The existence of positive solutions is established by a degree argument together with a priori estimates. In the special case the boundary value problem in , and on is considered. Finally the eigenvalue problem in , and on is studied looking for a branch of positive solutions bifurcating from the line of trivial solutions , .