Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON NONLINEAR ELLIPTIC EQUATIONS WITH SINGULAR LOWER ORDER TERM

  • Marah, Amine (Faculte des Sciences Et Techniques Morocco Universite Hassan 1) ;
  • Redwane, Hicham (Faculte des Sciences Juridiques 'Economiques et Sociales Universite Hassan 1)
  • Received : 2020.04.04
  • Accepted : 2020.08.21
  • Published : 2021.03.31
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Abstract

We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like $$\{-div\((a(x)+{\mid}u{\mid}^q){\nabla}u\)=\frac{f}{{\mid}u{\mid}^{\gamma}}{\text{ in }}{\Omega},\\{u=0\;on\;{\partial}{\Omega},$$ where Ω is a bounded open subset of ℝℕ(N ≥ 2), a(x) is a measurable nonnegative function, q, �� > 0 and the source f is a nonnegative (not identicaly zero) function belonging to Lm(Ω) for some m ≥ 1. Our results will depend on the summability of f and on the values of q, �� > 0.

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References

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