Quasilinear equations with natural growth
David Arcoya, Pedro J. Martínez−Aparicio · Revista Matemática Iberoamericana · 2008
We study the existence of positive solution w\in H_0^1(\Omega) of the quasilinear equation -\Delta w+ g(w)| abla w|^2=a(x) , x\in \Omega , where \Omega is a bounded domain in \mathbb R^N , 0\leq a\in L^\infty (\Omega ) and g is a nonnegative continuous function on (0,+\infty) which may have a singularity at zero.