Opuscula Math. 32, no. 4 (2012), 775-781
http://dx.doi.org/10.7494/OpMath.2012.32.4.775

Opuscula Mathematica

# On the solvability of Dirichlet problem for the weighted p-Laplacian

Ewa Szlachtowska

Abstract. The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted $$p$$-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.

Keywords: $$p$$-Laplacian, weak solutions, solvability.

Mathematics Subject Classification: 35A15, 35J20, 35J60.

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• Ewa Szlachtowska
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland.
• Revised: 2012-03-19.
• Accepted: 2012-03-20.