Phuong Le, Vu Ho
We prove that all entire stable solutions of weighted quasilinear problem
must be zero. The result holds true for and . Here and is a new critical exponent, which is infinity in low dimension and is always larger than the classic critical one, while are nonnegative functions such that and for large |x|. We also construct an example to show the sharpness of our result.
Submitted July 11, 2017. Published March 15, 2018.
Math Subject Classifications: 35B53, 35J92, 35B08, 35B35.
Key Words: Quasilinear problems; stable solutions; Lane-Emden nonlinearity; Liouville theorems.
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| Phuong Le |
Department of Mathematical Economics
Banking University of Ho Chi Minh City, Vietnam
| Vu Ho |
Division of Computational Mathematics and Engineering
Institute for Computational Science
Ton Duc Thang University, Ho Chi Minh City, Vietnam
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