Existence and nonexistence of positive solutions of p-Kolmogorov equations perturbed by a Hardy potential
Abstract
In this article, we establish the phenomenon of existence and nonexistence of positive weak solutions of parabolic quasi-linear equations perturbed by a singular Hardy potential on the whole Euclidean space depending on the controllability of the given singular potential. To control the singular potential we use a weighted Hardy inequality with an optimal constant, which was recently discovered in Hauer and Rhandi (2013). Our results in this paper extend the ones in Goldstein et al. (2012) concerning a linear Kolmogorov operator significantly in several ways: firstly, by establishing existence of positive global solutions of singular parabolic equations involving nonlinear operators of p-Laplace type with a nonlinear convection term for 1
Publication Title
Nonlinear Analysis, Theory, Methods and Applications
Recommended Citation
Goldstein, J., Hauer, D., & Rhandi, A. (2016). Existence and nonexistence of positive solutions of p-Kolmogorov equations perturbed by a Hardy potential. Nonlinear Analysis, Theory, Methods and Applications, 131, 121-154. https://doi.org/10.1016/j.na.2015.07.016
