Opuscula Math. 40, no. 4 (2020), 483-494

Opuscula Mathematica

Properties of solutions to some weighted p-Laplacian equation

Prashanta Garain

Abstract. In this paper, we prove some qualitative properties for the positive solutions to some degenerate elliptic equation given by \[-\text{div}\big(w|\nabla u|^{p-2}\nabla u\big)=f(x,u),\quad w\in \mathcal{A}_p,\] on smooth domain and for varying nonlinearity \(f\).

Keywords: \(p\)-Laplacian, degenerate elliptic equations, weighted Sobolev space.

Mathematics Subject Classification: 35A01, 35J62, 35J70.

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  • Communicated by Patrizia Pucci.
  • Received: 2019-06-03.
  • Revised: 2020-03-20.
  • Accepted: 2020-05-18.
  • Published online: 2020-07-09.
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Cite this article as:
Prashanta Garain, Properties of solutions to some weighted p-Laplacian equation, Opuscula Math. 40, no. 4 (2020), 483-494, https://doi.org/10.7494/OpMath.2020.40.4.483

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