Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition

Abstract

Abstract We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450, 2013) and (Abstr. Appl. Anal. 2014:593210, 2014).

Keywords

• Weighted higher-order elliptic system
• Liouville-type theorem
• Navier boundary value
• Superharmonic property