Liouville Theorem for Lane Emden Equation of Baouendi Grushin operators

Abstract

In this paper, we establish a Liouville theorem for solutions to the Lane Emden equation involving Baouendi Grushin operators. We focus on solutions that are stable outside a compact set. Specifically, we prove that when p is smaller than the Joseph Lundgren exponent and differs from the Sobolev exponent, 0 is the unique solution stable outside a compact set. This work extends the results obtained by Farina (J. Math. Pures Appl., 87 (5) (2007)).

Theorems & Definitions (16)

• Theorem 1.1
• Corollary 1.1
• Proposition 2.1
• proof
• Definition 3.1
• Remark 3.1
• Lemma 3.1
• proof
• Remark 3.2
• proof : Proof of (1) in Theorem \ref{['thm1']}