An optimal Liouville-type theorem of the quasilinear parabolic equation with a -Laplace operator

摘要: Abstract In this paper, we consider nonnegative solutions of the quasilinear parabolic equation with p -Laplace operator u t = div ( | ∇ − 2 ) + q 1 , where > and . Our main result is that there no nontrivial positive bounded radial entire solution. The proof based on intersection comparison arguments, which can be viewed as a sophisticated form maximum principle has been used to deal semilinear heat by Polacik Quittner [Peter Polacik, Pavol Quittner, A Liouville-type theorem decay equation, Nonlinear Analysis TMA 64 (2006) 1679–1689] porous medium Souplet [Ph. Souplet, An optimal for source, J. Differential Equations 246 (2009) 3980–4005].