A LIOUVILLE TYPE THEOREM FOR KIRCHHOFF ELLIPTIC EQUATIONS INVOLVING ΔΛ OPERATORS

Abstract

In this paper, we study the Kirchhoff elliptic equations
−???? ( ||∇_????????||² ) Δ_???????? = −????^−????????(????) in ℝ^????,
where Δ???? is the degenerate Δ???? operator in ℝ????, ???? ≥ 3, the exponent ???? > 0, and ????(????) is aweight function. We establish a Liouville type theorem for the class of continuous positive stable solutions. In particular, our results improve existing results in [11] and [13].