Accepted Paper

Inserted: 5 nov 2020
Last Updated: 5 nov 2020

Journal: Journal of Functional Analysis
Year: 2020
Doi: https://doi.org/10.1016/j.jfa.2020.108787

Abstract:

We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.