Stable solutions to weighted quasilinear problems of lane-emden type
Stable solutions to weighted quasilinear problems of lane-emden type
Source title:
Electronic Journal of Differential Equations, 2018(71): 1-11,
2018
(ISI)
Academic year of acceptance:
2018-2019
Abstract:
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.