Quasilinear equations with natural growth

  • David Arcoya

    Universidad de Granada, Spain
  • Pedro J. Martínez-Aparicio

    Universidad de Granada, Spain


We study the existence of positive solution wH01(Ω)w\in H_0^1(\Omega) of the quasilinear equation Δw+g(w)w2=a(x)-\Delta w+ g(w)|\nabla w|^2=a(x), xΩx\in \Omega, where Ω\Omega is a bounded domain in RN\mathbb R^N, 0aL(Ω)0\leq a\in L^\infty (\Omega ) and gg is a nonnegative continuous function on (0,+)(0,+\infty) which may have a singularity at zero.

Cite this article

David Arcoya, Pedro J. Martínez-Aparicio, Quasilinear equations with natural growth. Rev. Mat. Iberoam. 24 (2008), no. 2, pp. 597–616

DOI 10.4171/RMI/548