LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

doi:10.1007/s10473-019-0202-x

Abstract

Abstract: This paper is devoted to the quasilinear equation

where p ≥ 2, Ω is a (bounded or unbounded) domain of R^N, w₁, w₂ are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω, w₁, w₂ and f, which extends and unifies several results on this topic.

Key words: quasilinear equations, stable solutions, nonexistence, Liouville theorems

Phuong LE, Vu HO. LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS[J].Acta mathematica scientia,Series B, 2019, 39(2): 357-368.

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