Opuscula Math. 33, no. 4 (2013), 701-711
http://dx.doi.org/10.7494/OpMath.2013.33.4.701

Opuscula Mathematica

# Picone-type identity and comparison results for a class of partial differential equations of order 4m

Jaroslav Jaroš

Abstract. In the paper, a Picone-type identity for the weighted $$p$$-polyharmonic operator is established and comparison theorems and other qualitative results for a class of half-linear partial differential equations of the $$4m$$th order based on this identity are derived.

Keywords: $$p$$-polyharmonic operator, Picone's identity.

Mathematics Subject Classification: 35B05, 35J70.

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• Jaroslav Jaroš
• Comenius University, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, 842 48 Bratislava, Slovakia
• Revised: 2013-04-19.
• Accepted: 2013-04-25.