Thanks to a change of unknown we compare two elliptic quasilinear problems with Dirichlet data in a bounded domain of $\mathbb{ R}^{ N}.$ The first one, of the form $-\Delta_{ p}u=\beta(u)| \nabla u| ^{ p}+\lambda f(x),$ where $\beta$ is nonnegative, involves a gradient term with natural growth. The second one, of the form $-\Delta_{ p}v=\lambda f(x)(1+g(v))^{ p-1}$ where $g$ is nondecreasing, presents a source term of order 0. The correlation gives new results of existence, nonexistence and multiplicity for the two problems.
Categories: math.AP