Anh Tuan Duong, Nhu Thang Nguyen
Abstract:
In this article, we study the equation
where
(resp.,
)
is Grushin operator
(resp. Grushin gradient), p>1 and
.
The scalar function w satisfies a decay condition,
and
is the norm corresponding to the Grushin distance.
Based on the approach by Farina [8], we establish a Liouville
type theorem for the class of stable sign-changing weak solutions.
In particular, we show that the nonexistence result for stable positive
classical solutions in [4] is still valid for the above equation.
Submitted January 19, 2017. Published April 25, 2017.
Math Subject Classifications: 35J61, 35B53.
Key Words: Liouville type theorem; stable weak solution; Grushin operator;
degenerate elliptic equation.
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Anh Tuan Duong Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay, Ha noi, Viet Nam email: tuanda@hnue.edu.vn | |
Nhu Thang Nguyen Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay, Ha noi, Viet Nam email: thangnn@hnue.edu.vn |
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