Opuscula Math. 40, no. 4 (2020), 483-494
https://doi.org/10.7494/OpMath.2020.40.4.483

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.
• Revised: 2020-03-20.
• Accepted: 2020-05-18.
• Published online: 2020-07-09.