Singular quasilinear equations with quadratic growth in the gradient without sign condition ✩

@inproceedings{Arcoya2008SingularQE,
  title={Singular quasilinear equations with quadratic growth in the gradient without sign condition ✩},
  author={David Arcoya and Sara Barile and Pedro J. Mart{\'i}nez-Aparicio},
  year={2008}
}
  • David Arcoya, Sara Barile, Pedro J. Martínez-Aparicio
  • Published 2008
a r t i c l e i n f o a b s t r a c t Keywords: Singular quasilinear elliptic equations Quadratic growth in the gradient Positive solutions Given a bounded domain Ω in R N , and a function a ∈ L q (Ω) with q > N/2, we study the existence of a positive solution for the quasilinear problem −w + g(x, w)|∇ w| 2 = a(x), x ∈ Ω, w ∈ H 1 0 (Ω), where g(x, s) is a Carathéodory function on Ω × (0, +∞) which may have a singularity at s = 0 and may change of sign. 

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